Systems and methods for planning an orthodontic treatment

ABSTRACT

Methods and systems for determining an orthodontic treatment for a subject are provided. The methods comprises: acquiring a 3D representation of an arch form including that of a gingiva of the subject; obtaining a plurality of segmentation loops; determining, between each pair of adjacent segmentation loops of the plurality of segmentation loops, a midpoint, thereby generating a plurality of primary midpoints; based on the plurality of midpoints, generating a primary central curve; generating, based on the primary central curve, a first inner mesh curve and a first outer mesh curve; generating a first segment of the reconstructed 3D representation of the gingiva by joining each one from the plurality of primary midpoints with respective ones from the first plurality of inner midpoints and from the first plurality of outer midpoints; and causing display of the first segment of the reconstructed 3D representation of the gingiva.

CROSS-REFERENCE

The present application is a continuation of U.S. patent applicationSer. No. 16/938,141 filed Jul. 24, 2020, the entirety of which isincorporated by reference.

FIELD

The present technology relates to systems and methods for planning anorthodontic treatment for a patient, in general; and more specifically,to systems and methods for reconstructing a gingiva of the patient.

BACKGROUND

Orthodontic treatment plans for treating malocclusion disorders of asubject (or for assessing efficacy of an already ongoing one), typicallyuse various anthropometric parameters associated with a subject's skull,such as those associated with a subject's teeth (including crownportions and root portions thereof), and a subject's gingiva. Suchparameters may be, for example, obtained or otherwise, determinedthrough analyzing corresponding image data.

For example, by applying intra-oral scanning techniques, a 3D model ofan arch form of the subject may be obtained, which may further include3D models of the crown portions of the subject's teeth and a raw 3Dmodel of the subject's gingiva, and some of the anthropometricparameters (such as overall dimensions of the crown portions) may hencebe used for devising an orthodontic treatment. Further, a 3D model of aroot portion may be received to generate a 3D model of the given tooth.Such a 3D model of the given tooth may be used for modelling movementsof the given tooth considering spatial positions of the crown portionand the root portions thereof relative to crown portions and rootportions of other teeth in the course of the planned orthodontictreatment. However, for a more efficient and effective orthodontictreatment, it may also be necessary to consider the movements of thegiven tooth relative to the subject's gingiva, certain parameters ofwhich may thus be required. These parameters may include, for example,overall dimensions of the subject's gingiva, parameters indicative ofcurvature thereof in points of attachment thereof to the subject'steeth, such as gingival grooves, interdental papillae, and the like.

However, the intra-oral scanning techniques may be ineffective forcapturing a comprehensive 3D model of the subject's gingiva as they canbe limited by anatomical specifics of the subject. For example, someportions of the subject's gingiva may be simply inaccessible to anintra-oral scanner as being obstructed by other anatomical structures ofthe subject's skull, such as muscles, bones, and junctions, which causesthe so scanned 3D model of the subject's gingiva (also, referred toherein as a “raw 3D model” of the subject's gingiva) to have unevenedges (producing, in a sense, a “torn out” 3D model of the subject'sgingiva). As a result, modelling the movements of the subject's teeth,based on such a raw 3D model of the subject's gingiva, inaccuratelyrepresentative thereof, may, for example, be associated with causingdiscomfort to the subject, or even damages to the subject's gingiva(including tissues around it, such as proximal blood vessels and nervepathways, for example) during receiving the orthodontic treatment.Furthermore, using the raw 3D model of the subject's gingiva forproducing aligners may result in low quality thereof.

Accordingly, additional image data indicative of the subject's gingivamay be required. The additional image data may be obtained via the useof other imaging techniques, such as computer tomography (CT), magneticresonance (MR) imaging, or panoramic radiography, for example.

However, these techniques and the associated apparatuses may not bereadily available to the practitioners to obtain such data. Further,even if timely access to the additional image data is available, itcould be computationally expensive to merge it with the 3D model of thegiven tooth maintaining certain level of quality of the resultingorthodontic treatment, which may significantly reduce efficiency of suchan approach.

Certain prior art approaches have been proposed to tackle theabove-identified technical problem, which are directed to reconstructingthe 3D model of the subject's gingiva based on a dental segmentationcurve.

Chinese Patent Application Publication No.: 103,700,103-A filed on Dec.5, 2013, assigned to Jiaxing University, and entitled “Method forAutomatically Extracting Gingiva Curves of Three-Dimensional DigitalDentition Model” discloses a method for automatically extracting gingivacurves on a three-dimensional digital dentition model. The methodcomprises the steps of model positioning, gingival feature line search,gingival feature line partitioning and inter-tooth space gingival lineinterference analysis. The method is high in automatic degree, enclosedgingival curves around each tooth on the dentition model can beconstructed rapidly and accurately, the problems of low efficiency, pooraccuracy and the like existing in the conventional manual design aresolved effectively, and the efficiency and attractiveness of oralrehabilitation are improved.

Chinese Patent No.: 105,662,610-B issued on Mar. 13, 2018, assigned toQingdao Labsys Medical Technology Co., Ltd, and entitled “The GenerationMethod of the Virtual Gum for Stealthy Correction Based on Model”discloses a method of generation of the virtual gum for stealthycorrection based on model, the series of parameters that gained can besplit according to actual teeth model generate virtual gum in acomputer. The virtual gum generated using the method for the presentinvention is more true, but simplifies many Extraneous details, is shownrescuing software, and invisible orthotic device makes etc. is widelyused. And the gum fine degree generated can be controlled by changingparameter, it can be refined or simplified according to different needs,with suitable for the equipment under the conditions of differenthardware.

SUMMARY

It is an object of the present technology to ameliorate at least some ofthe inconveniences present in the prior art.

Developers of the present technology have devised methods and systemsfor generating a comprehensive 3D representation of the arch form of thesubject including 3D model of the subject's teeth and the comprehensive3D model of the subject's gingiva.

This may include, first, reconstructing the 3D model of the crownportion of the given tooth based on a raw 3D model of the crown portionthereof, which may further include identifying and removing certainimage artefacts (also referred to herein as “digital garbage” or“undesired portions” of the raw 3D model), that is, portions of the raw3D model of the crown portion forming no part of the actualconfiguration of the crown portion of the given tooth and generated,inter alia, due to technical flaws associated with the intra-oralscanning techniques used for capturing the raw 3D model of the crownportion. For example, these image artefacts may typically be found inportions of the raw 3D model of the crown portions associated withinterdental spaces. In this regard, the 3D model of the crown portionfree of the image artefacts may be representative of a more anatomicallyaccurate contour thereof, which may hence allow for a more accuratemodelling of movements of the crown portion of the given tooth withinthe subject's arch form, for example avoiding collisions thereof withother crown portions. Also, the so generated 3D model of the crownportion may further allow generating a more accurate parametricequivalent model of the root portion, higher accuracy of which mayenable to model the movements of the given tooth as a whole morepredictably in the course of the orthodontic treatment.

Second, based on the so generated 3D model of the crown portion, the 3Dmodel of the root portion may be generated. In this regard, thedevelopers have realized that the 3D model of the root portion may be aparametric equivalent model thereof, which may be indicative of certainspecific parameters of the actual root portion of the given toothcurrently needed to determine the orthodontic treatment. Further, the 3Dmodel of the given tooth may further be generated by merging theparametric equivalent model of the root portion and the augmented 3Dmodel of the crown portion of the given tooth. Accordingly, theso-generated 3D model of the given tooth may further be used, forexample, for determining a force system to be imposed on the given toothto cause it to move into a position associated with alignment thereofwithin a subject's arch form.

Thus, the 3D model of the given tooth may be used for modelling sodetermined movements of the given tooth in the course of the entireorthodontic treatment, and for accounting for interactions of the giventooth with other teeth adjacent thereto more comprehensively.

Finally, the reconstructing the comprehensive 3D model of the subject'sgingiva may be based on a raw 3D model thereof and so reconstructed 3Dmodels of the crown portions. The developers have appreciated that thecomprehensive 3D model of the subject's gingiva may be more accuratelyreconstructed based on considering certain curves derived from the raw3D model thereof. More specifically, the developers have realized that acentral curve (also referred to herein as “a primary central curve”)generated based on points specifically identified, on the raw 3D modelof the subject's gingiva, between segmentation loops associated with thesubject's teeth. The primary central curve may further be used forconstructing respective inner and outer curves in associated parallelhorizontal planes, which, when joined, allow for generating thecomprehensive 3D model of the subject's gingiva. Thus, the so generatedcomprehensive 3D model of the subject's gingiva may be representative ofa more anatomically accurate contour thereof allowing for effectivelyconsidering movements of the root portion of the given tooth in thesubject's gingiva, thereby avoiding damages to the subject's gingiva andcausing discomfort to the subject.

Therefore, such a comprehensive 3D model of the subject's gingivaaccurately representing an actual anatomical configuration thereof mayallow for determining a safer and more effective orthodontic treatmentfor the subject.

Further, the comprehensive 3D model of the subject's gingiva may allowfor a more computationally efficient approach to applying textures andcolours thereto for more effective visualization thereof on a screen ofa computer system increasing accuracy of the planned orthodontictreatment.

Finally, the comprehensive 3D model of the subject's gingiva, as havingoverall dimensions corresponding to actual dimensions of the subject'sgingiva, may allow for a more efficient planning of material consumptionused for producing (for example, by means of 3D printing) aligners (suchas those made from composite materials).

Non-limiting embodiments of the present technology are directed tomethods and systems for generating a comprehensive 3D model of thesubject's arch form including (i) generating the 3D model of the crownportion of the given tooth, based on the raw 3D model thereof, (ii)generating the parametric equivalent model for the root portion of thegiven tooth based on the 3D model of the crown portion thereof andcertain reference data associated therewith, and (iii) generating thecomprehensive 3D model of the subject's gingiva based on the raw 3Dmodel thereof. These methods and systems allow generating thecomprehensive 3D model of the subject's arch form avoiding the need forobtaining the additional image data, for example, that representative ofthe root portion of the given tooth and hidden portions of the subject'sgingiva, such as CT/MR scans or a panoramic radiograph, for example.

Therefore, such an approach to reconstructing the comprehensive 3D modelof the subject's arch form allows manipulating the level of granularityand detail of the so reconstructed model depending on a specific task athand associated with the orthodontic treatment determination processusing a minimum of image data, which eventually allows for a moreeffective and efficient use of computational resources.

Therefore, according to a first broad aspect of the present technology,there is provided a method for providing an augmented 3D representationof a given tooth of a patient. The method is executable by a processor.The method comprises: acquiring a raw 3D representation of an arch formof the patient, the arch form comprising a gingiva and at least onetooth of the patient, the raw 3D representation comprising a definedportion forming part of a surface of the given tooth, and at least oneundefined portion not forming part of the surface of the given tooth;the raw 3D representation comprising a 3D mesh having a plurality ofvertices comprising: constrained vertices associated with the definedportion, each constrained vertex having a normal constrained vertexvector; unconstrained vertices initially associated with the undefinedportion, each unconstrained vertex having a normal unconstrained vertexvector; generating a set of confirmed constrained vertices, includingthe constrained vertices associated with the defined portion, forproviding the augmented 3D representation of the given tooth by:iteratively, for a given constrained vertex, identifying at least oneassociated unconstrained vertex which is adjacent to the givenconstrained vertex in the 3D mesh; determining an angular differencebetween the normal constrained vertex vector of the given constrainedvertex and the normal unconstrained vertex vector of the at least oneassociated unconstrained vertex; in response to the angular differencebeing equal to or below a predetermined threshold value: identifying theat least one associated unconstrained vertex to be a constrained vertexassociated with the defined portion for inclusion in the set ofconfirmed constrained vertices; in response to the angular differencebeing above the predetermined threshold value: identifying the at leastone associated unconstrained vertex to be an unconstrained vertexassociated with the undefined portion for exclusion from the set ofconfirmed constrained vertices; causing display of the augmented 3Drepresentation of the given tooth based on the set of confirmedconstrained vertices.

In some implementations of the method, the causing display of theaugmented 3D representation comprises: performing a smoothing operationon the set of confirmed constrained vertices to generate a smoothsurface of the given tooth.

In some implementations of the method, the method comprises: causing afilling of any gaps in the set of confirmed constrained vertices by thesmoothing operation.

In some implementations of the method, the performing the smoothingoperation comprises applying a Harmonic Function.

In some implementations of the method, the defined portion and theundefined portion are determined by applying an erosion function to theraw 3D representation.

In some implementations of the method, the defined portion is determinedby: determining, based on the erosion function, an edge of the giventooth based on the raw 3D representation of the given tooth; anddetermining, based on the erosion function, a location of the definedportion by a predetermined distance, along a horizontal axis associatedwith the raw 3D representation of the given tooth, from at least onevertical edge of the raw 3D representation of the given tooth.

In some implementations of the method, the raw 3D representation is of aplurality of teeth of the patient including the given tooth, the methodfurther comprising segmenting the raw 3D representation to separate therepresentation of the given tooth from other teeth of the plurality ofteeth.

In some implementations of the method, the method further comprisesproviding a respective augmented 3D representation for other teeth ofthe plurality of teeth of the patient.

In some implementations of the method, the method further comprisesgenerating an orthodontic treatment plan based on the augmented 3Drepresentation of the given tooth.

In some implementations of the method, the raw 3D representation of thegiven tooth of the patient has a crown portion and a root portion, andthe defined portion is based on one or more of the crown portion and theroot portion.

According to a second broad aspect of the present technology, there isprovided a system for providing an augmented 3D representation of agiven tooth of a patient. The system comprises a processor configured toexecute a method. The method comprises: acquiring a raw 3Drepresentation of an arch form of the patient, the arch form comprisinga gingiva and at least one tooth of the patient, the raw 3Drepresentation comprising a defined portion forming part of a surface ofthe given tooth, and at least one undefined portion not forming part ofthe surface of the given tooth; the raw 3D representation comprising a3D mesh having a plurality of vertices comprising: constrained verticesassociated with the defined portion, each constrained vertex having anormal constrained vertex vector; unconstrained vertices initiallyassociated with the undefined portion, each unconstrained vertex havinga normal unconstrained vertex vector; generating a set of confirmedconstrained vertices, including the constrained vertices associated withthe defined portion, for providing the augmented 3D representation ofthe given tooth by: iteratively, for a given constrained vertex,identifying at least one associated unconstrained vertex which isadjacent to the given constrained vertex in the 3D mesh; determining anangular difference between the normal constrained vertex vector of thegiven constrained vertex and the normal unconstrained vertex vector ofthe at least one associated unconstrained vertex; in response to theangular difference being equal to or below a predetermined thresholdvalue: identifying the at least one associated unconstrained vertex tobe a constrained vertex associated with the defined portion forinclusion in the set of confirmed constrained vertices; in response tothe angular difference being above the predetermined threshold value:identifying the at least one associated unconstrained vertex to be anunconstrained vertex associated with the undefined portion for exclusionfrom the set of confirmed constrained vertices; causing display of theaugmented 3D representation of the given tooth based on the set ofconfirmed constrained vertices.

In some implementations of the system, the causing display of theaugmented 3D representation comprises: performing a smoothing operationon the set of confirmed constrained vertices to generate a smoothsurface of the given tooth.

In some implementations of the system, the method further comprises:causing a filling of any gaps in the set of confirmed constrainedvertices by the smoothing operation.

In some implementations of the system, wherein the performing thesmoothing operation comprises applying a Harmonic Function.

In some implementations of the system, the defined portion and theundefined portion are determined by applying an erosion function to theraw 3D representation.

In some implementations of the system, the defined portion is determinedby: determining, based on the erosion function, an edge of the giventooth based on the raw 3D representation of the given tooth; anddetermining, based on the erosion function, a location of the definedportion by a predetermined distance, along a horizontal axis associatedwith the raw 3D representation of the given tooth, from at least onevertical edge of the raw 3D representation of the given tooth.

In some implementations of the system, the raw 3D representation is of aplurality of teeth of the patient including the given tooth, the methodfurther comprising segmenting the raw 3D representation to separate therepresentation of the given tooth from other teeth of the plurality ofteeth.

In some implementations of the system, the processor is furtherconfigured to provide a respective augmented 3D representation for otherteeth of the plurality of teeth of the patient.

In some implementations of the system, the processor is furtherconfigured to generate an orthodontic treatment plan based on theaugmented 3D representation of the given tooth.

According to a third broad aspect of the present technology, there isprovided a method for determining an orthodontic treatment based ongenerating a 3D representation of a given tooth of a subject. The giventooth includes a crown portion and a root portion. The method isexecutable by a processor. The method comprises: acquiring a 3Drepresentation of the crown portion of the given tooth, the 3Drepresentation of the crown portion being associated with apredetermined longitudinal tooth axis; generating a 3D representation ofthe root portion of the given tooth by executing the steps of:determining a location of a root apex of the 3D representation of theroot portion relative to the predetermined longitudinal tooth axis, thedetermining being based on a predetermined instruction for locating theroot apex; generating, in a reference plane dissecting the predeterminedlongitudinal tooth axis and based on the 3D representation of the crownportion, a closed curve on the 3D representation of the crown portion,segmenting the closed curve into a plurality of sub-curves; for each oneof the plurality of sub-curves, based on the root apex and thepredetermined longitudinal tooth axis, generating a respective segmentof a plurality of segments of the 3D representation of the root portion,the plurality of segments of the 3D representation of the root portioncomprising a totality thereof; merging the 3D representation of thecrown portion with the 3D representation of the root portion, therebygenerating the 3D representation of the given tooth; and determining,based on the 3D representation of the given tooth, the orthodontictreatment for the subject.

In some implementations of the method, the predetermined longitudinaltooth axis is a central tooth axis of the given tooth having beenpredetermined based on the 3D representation of the crown portion.

In some implementations of the method, the predetermined instruction forlocating the root apex is based on reference data associated with thegiven tooth, the reference data comprising data of an approximate rootlength associated with the given tooth.

In some implementations of the method, the 3D representation of thecrown portion comprises a 3D mesh having a plurality of vertices, andthe generating, in the reference plane, the closed curve furthercomprising: projecting each of the plurality of vertices into thereference plane, thereby generating a plurality of projected vertices;and generating the closed curve on and around the 3D representation ofthe crown portion to include most distant ones of the plurality ofprojected vertices from the predetermined longitudinal tooth axis.

In some implementations of the method, the reference plane isperpendicular to the predetermined longitudinal tooth axis.

In some implementations of the method, the reference plane is positionedalong the predetermined longitudinal tooth axis at a predetermineddistance based on a height of the 3D representation of the crownportion.

In some implementations of the method, each one of the plurality ofsub-curves is of a same length.

In some implementations of the method, the generating the respectivesegment of the 3D representation of the root portion is based on arespective Bezier curve extending between one of edges associated withthe respective one of the plurality of sub-curves and the root apex.

In some implementations of the method, the respective segment of the 3Drepresentation of the root portion is a segment of a revolution surfacegenerated by revolving the respective Bezier curve about thepredetermined longitudinal tooth axis.

In some implementations of the method, the method comprises augmentingthe 3D representation of the root portion based on a respectiveparametric root model associated with the given tooth; and causingdisplay of the 3D representation of the given tooth.

In some implementations of the method, the given tooth is one of aplurality of teeth of the subject, and the method further comprises:generating a respective 3D representation of each of the plurality ofteeth of the subject to be included in a 3D representation of asubject's arch form; and executing a collision prevention algorithm forpreventing intersection of the 3D representation of the given tooth witha 3D representation of an adjacent thereto one of the plurality of teethwithin the 3D representation of the subject's arch form.

According to a fourth broad aspect of the present technology, there isprovided a system for determining an orthodontic treatment based ongenerating a 3D representation of a given tooth of a subject. The giventooth includes a crown portion and a root portion. The system comprisesa processor configured to execute a method comprising: acquiring a 3Drepresentation of the crown portion of the given tooth, the 3Drepresentation of the crown portion being associated with apredetermined longitudinal tooth axis; generating a 3D representation ofthe root portion of the given tooth by executing the steps of:determining a location of a root apex of the 3D representation of theroot portion relative to the predetermined longitudinal tooth axis, thedetermining being based on a predetermined instruction for locating theroot apex; generating, in a reference plane dissecting the tooth axisand based on the 3D representation of the crown portion, a closed curveon or around the 3D representation of the crown portion, segmenting theclosed curve into a plurality of sub-curves; for each one of theplurality of sub-curves, based on the root apex and the predeterminedlongitudinal tooth axis, generating a respective segment of a pluralityof segments of the 3D representation of the root portion, the pluralityof segments of the 3D representation of the root portion comprising atotality thereof; merging the 3D representation of the crown portionwith the 3D representation of the root portion, thereby generating the3D representation of the given tooth; and determining, based on the 3Drepresentation of the given tooth, the orthodontic treatment for thesubject.

In some implementations of the system, the predetermined longitudinaltooth axis is a central tooth axis of the given tooth having beenpredetermined based on the 3D representation of the crown portion.

In some implementations of the system, the predetermined instruction forlocating the root apex is based on reference data associated with thegiven tooth, the reference data comprising data of an approximate rootlength associated with the given tooth.

In some implementations of the system, wherein the 3D representation ofthe crown portion comprises a 3D mesh having a plurality of vertices,and the generating, in the reference plane, the closed curve furthercomprising: projecting each of the plurality of vertices into thereference plane, thereby generating a plurality of projected vertices;and generating the closed curve on and around the 3D representation ofthe crown portion to include most distant, from the predeterminedlongitudinal tooth axis, ones of the plurality of projected vertices.

In some implementations of the system, the reference plane isperpendicular to the predetermined longitudinal tooth axis; and thereference plane is further translated along the predeterminedlongitudinal tooth axis at a predetermined distance determined based ona height of the 3D representation of the crown portion.

In some implementations of the system, each one of the plurality ofsub-curves is of a same length.

In some implementations of the system, the generating the respectivesegment of the 3D representation of the root portion is based on arespective Bezier curve extending between one of edges associated withthe respective one of then plurality of sub-curves and the root apex;and the respective segment of the 3D representation of the root portionis a segment of a revolution surface generated by revolving therespective Bezier curve about the predetermined longitudinal tooth axis.

In some implementations of the system, the processor is furtherconfigured to: augment the 3D representation of the root portion basedon a respective parametric root model associated with the given tooth;and cause display of the 3D representation of the given tooth.

In some implementations of the system, the given tooth is one of aplurality of teeth of the subject, and the processor being furtherconfigured: generate a respective 3D representation of each of theplurality of teeth of the subject to be included in a 3D representationof a subject's arch form; and execute a collision prevention algorithmfor preventing intersection of the 3D representation of the given toothwith a 3D representation of an adjacent thereto one of the plurality ofteeth within the 3D representation of the subject's arch form.

According to a fifth broad aspect of the present technology, there isprovided a method for reconstructing a 3D representation of a gingivaassociated with an arch form of a subject. The method is executed by aprocessor. The method comprises: acquiring a 3D representation of anarch form associated with the subject, the 3D representation including arepresentation of the gingiva and a plurality of teeth of the subject;the 3D representation of the arch form including data of a transverseplane associated with a skull of the subject; the transverse plane beingassociated with a common median axis lying therein and a common verticalaxis perpendicular thereto; segmenting, in the 3D representation of thearch form, associated representations of the plurality of teeth and thegingiva to generate a plurality of segmentation loops, each segmentationloop being respectively associated with each tooth of the plurality ofteeth and representing an interface of a given tooth with the gingiva;determining, between each adjacent two segmentation loops of theplurality of segmentation loops, a midpoint, thereby generating aplurality of primary midpoints for the plurality of segmentation loops;based on the plurality of midpoints, generating a primary central curve.Thus, the primary central curve may be bisected by the common medianaxis. The method further comprises: generating, based on the primarycentral curve, a first inner mesh curve and a first outer mesh curve,the first inner mesh curve positioned along a first horizontal plane andthe first outer mesh curve positioned along a second horizontal plane,both the first horizontal plane and the second horizontal plane beingparallel to the transverse plane and being vertically offset, along thecommon vertical axis, from a highest vertex of the plurality ofsegmentation loops; the first inner mesh curve being offset along thecommon median axis posteriorly relative to the primary central curvealong the first horizontal plane; and the first outer mesh curve beingoffset along the common median axis anteriorly relative to the primarycentral curve along the second horizontal plane; projecting theplurality of primary midpoints onto the first inner mesh curve and thefirst outer mesh curve, thereby generating a first plurality of innermidpoints and a first plurality of outer midpoints; generating a firstsegment of the reconstructed 3D representation of the gingiva by joiningeach one from the plurality of primary midpoints with respective onesfrom the first plurality of inner midpoints and from the first pluralityof outer midpoints; and causing display of the first segment of thereconstructed 3D representation of the gingiva.

In some implementations of the method, the first horizontal plane andthe second horizontal plane comprise a same horizontal plane.

In some implementations of the method, the first horizontal plane andthe second horizontal plane are vertically offset, along the commonvertical axis, relative to each other.

In some implementations of the method, the projecting the plurality ofprimary midpoints onto the first inner mesh curve and the first outermesh curve is based on respective proportional coefficients, a given oneof the respective proportional coefficients being indicative of a ratiobetween a length of the primary central curve and that of a respectiveone of the first inner mesh curve and the first outer mesh curve.

In some implementations of the method, the method further comprisesgenerating a second segment of the reconstructed 3D representation ofthe gingiva by: generating, based on the primary central curve, a secondinner mesh curve and a second outer mesh curve, the second inner meshcurve being positioned along a third horizontal plane and the secondouter mesh curve being positioned along a fourth horizontal plane, thethird horizontal plane being parallel to and vertically offset from thefirst horizontal plane and the fourth horizontal plane being parallel toand vertically offset from the second horizontal plane; the second innermesh curve being offset along the common median axis posteriorlyrelative to the primary central curve along the third horizontal plane;and the second outer mesh curve being offset along the common medianaxis anteriorly relative to the primary central curve along the fourthhorizontal plane; projecting the plurality of primary midpoints onto thesecond inner mesh curve and the second outer mesh curve, therebygenerating a second plurality of inner midpoints and a second pluralityof outer midpoints; and generating a second segment of the reconstructed3D representation of the gingiva by joining each one from the pluralityof primary midpoints with respective ones from the second plurality ofinner midpoints and from the second plurality of outer midpoints.

In some implementations of the method, the method further comprisescausing display of the first and second segments of the reconstructed 3Drepresentation of the gingiva.

In some implementations of the method, each segmentation loop of theplurality of segmentation loops is generated by: generating apreliminary segmentation loop based on segmentation of respectiverepresentations of the gingiva and the plurality of teeth on the 3Drepresentation of the arch form; identifying in the preliminarysegmentation loop a plurality of vertices; and adjusting a distancebetween at least some of the vertices, to generate the segmentationloop.

In some implementations of the method, the segmenting comprises applyingone or more of the following functions: thresholding, clustering, edgedetection, smoothing, and closing the loop.

In some implementations of the method, the method further comprisesgenerating, between a given pair of adjacent segmentation loops of theplurality of segmentation loops, an outer arc and an inner arc forinterconnecting the given pair of adjacent segmentation loops, therebygenerating a primary border curve.

In some implementations of the method, the method further comprisesgenerating, between the given pair of adjacent segmentation loops of theplurality of segmentation loops, a tween curve originating in arespective one of the plurality of primary midpoints, the tween curveextending through the outer arc and the inner arc, thereby generating aplurality of tween curves; and wherein the joining each one from theplurality of primary midpoints with respective ones from the firstplurality of inner midpoints and from the first plurality of outermidpoints is based on a respective one of the plurality of tween curves.

In some implementations of the method, the distance between the at leastsome of the vertices is adjusted to be equal.

In some implementations of the method, the primary central curve isgenerated using a Bezier curve.

In some implementations of the method, the method further comprisesusing the reconstructed 3D representation of the gingiva to plan anorthodontic treatment.

In some implementations of the method, the 3D representation of thegingiva comprises a plurality of mesh elements which are not ordered,and wherein the generated 3D representation of the gingiva comprises aplurality of ordered mesh elements.

Finally, according to a sixth broad aspect of the present technology,there is provided a system for reconstructing a 3D representation of agingiva associated with an arch form of a subject. The system comprisesa processor configured to execute a method. The method comprises:acquiring a 3D representation of an arch form associated with thesubject, the 3D representation including a representation of the gingivaand a plurality of teeth of the subject; the 3D representation of thearch form including data of a transverse plane associated with a skullof the subject; the transverse plane being associated with a commonmedian axis lying therein and a common vertical axis perpendicularthereto; segmenting, in the 3D representation of the arch form,associated representations of the plurality of teeth and the gingiva togenerate a plurality of segmentation loops, each segmentation looprespectively associated with each tooth of the plurality of teeth andrepresenting an interface of a given tooth with the gingiva;determining, between each adjacent two segmentation loops of theplurality of segmentation loops, a midpoint, thereby generating aplurality of primary midpoints for the plurality of segmentation loops;based on the plurality of midpoints, generating a primary central curve.Thus, the primary central curve may be bisected by the common medianaxis. The method further comprises: generating, based on the primarycentral curve, a first inner mesh curve and a first outer mesh curve,the first inner mesh curve positioned along a first horizontal plane andthe first outer mesh curve positioned along a second horizontal plane,both the first horizontal plane and the second horizontal plane beingparallel to the transverse plane and being vertically offset, along thecommon vertical axis, from a highest vertex of the plurality ofsegmentation loops; the first inner mesh curve being offset along thecommon median axis posteriorly relative to the primary central curvealong the first horizontal plane; and the first outer mesh curve beingoffset along the common median axis anteriorly relative to the primarycentral curve along the second horizontal plane; projecting theplurality of primary midpoints onto the first inner mesh curve and thefirst outer mesh curve, thereby generating a first plurality of innermidpoints and a first plurality of outer midpoints; generating a firstsegment of the reconstructed 3D representation of the gingiva by joiningeach one from the plurality of primary midpoints with respective onesfrom the first plurality of inner midpoints and from the first pluralityof outer midpoints; and causing display of the first segment of thereconstructed 3D representation of the gingiva.

In some implementations of the system, the processor is furtherconfigured to generate a second segment of the reconstructed 3Drepresentation of the gingiva by: generating, based on the primarycentral curve, a second inner mesh curve and a second outer mesh curve,the second inner mesh curve and the second outer mesh curve beingpositioned along a third horizontal plane and a fourth horizontal plane,both the third horizontal plane and the fourth horizontal plane beingparallel to and vertical offset from the first horizontal plane and thesecond horizontal plane, respectively; the second inner mesh curve beingoffset along the common median axis posteriorly relative to the primarycentral curve along the third horizontal plane; and the second outermesh curve being offset along the common median axis anteriorly relativeto the primary central curve along the fourth horizontal plane;projecting the plurality of primary midpoints onto the second inner meshcurve and the second outer mesh curve, thereby generating a secondplurality of inner midpoints and a second plurality of outer midpoints;and generating a second segment of the reconstructed 3D representationof the gingiva by joining each one from the plurality of primarymidpoints with respective ones from the second plurality of innermidpoints and from the second plurality of outer midpoints.

In some implementations of the system, the processor is furtherconfigured to cause display of the first and second segments of thereconstructed 3D representation of the gingiva.

In some implementations of the system, each segmentation loop of theplurality of segmentation loops is generated by: generating apreliminary segmentation loop based on segmentation of respectiverepresentations of the gingiva and the plurality of teeth on the 3Drepresentation of the arch form; identifying in the preliminarysegmentation loop a plurality of vertices; and adjusting a distancebetween at least some of the vertices, to generate the segmentationloop.

In some implementations of the system, the processor is furtherconfigured to generate, between a given pair of adjacent segmentationloops of the plurality of segmentation loops, an outer arc and an innerarc for interconnecting the given pair of adjacent segmentation loops,thereby generating a primary border curve.

In some implementations of the system, the processor is furtherconfigured to generate, between the given pair of adjacent segmentationloops of the plurality of segmentation loops, a tween curve originatingin a respective one of the plurality of primary midpoints, the tweencurve extending through the outer arc and the inner arc, therebygenerating a plurality of tween curves; and wherein the joining each onefrom the plurality of primary midpoints with respective ones from thefirst plurality of inner midpoints and from the first plurality of outermidpoints is based on a respective one of the plurality of tween curves.

In the context of the present specification, unless expressly providedotherwise, a computer system may refer, but is not limited to, an“electronic device”, an “operation system”, a “system”, a“computer-based system”, a “controller unit”, a “control device” and/orany combination thereof appropriate to the relevant task at hand.

In the context of the present specification, unless expressly providedotherwise, the expression “computer-readable medium” and “memory” areintended to include media of any nature and kind whatsoever,non-limiting examples of which include RAM, ROM, disks (CD-ROMs, DVDs,floppy disks, hard disk drives, etc.), USB keys, flash memory cards,solid state-drives, and tape drives.

In the context of the present specification, a “database” is anystructured collection of data, irrespective of its particular structure,the database management software, or the computer hardware on which thedata is stored, implemented or otherwise rendered available for use. Adatabase may reside on the same hardware as the process that stores ormakes use of the information stored in the database or it may reside onseparate hardware, such as a dedicated server or plurality of servers.

In the context of the present specification, unless expressly providedotherwise, the words “first”, “second”, “third”, etc. have been used asadjectives only for the purpose of allowing for distinction between thenouns that they modify from one another, and not for the purpose ofdescribing any particular relationship between those nouns.

In the context of the present specification, the term “parametricequivalent model” of a given tooth (or of a specific portion thereof,such as a root portion thereof, for example) refers to a mathematicalmodel of the given tooth (such as a 3D mesh representation, for example)indicative of certain parameters of the given tooth determined eitherstatistically or analytically, such as, without limitation: overalldimensions of the given tooth, anatomical features thereof (a number ofroot branches, curvature thereof), solidity, and the like. Typically,the parametric equivalent model is indicative only of a limited numberof the parameters associated with the given tooth, needed at a presentphase of the orthodontic treatment for further planning thereof, Thus,the parametric equivalent model may be referred to as a simplified modelof the given tooth, as opposed to an anatomically accurate 3D model ofthe given tooth. Accordingly, using the parametric equivalent model ofthe given tooth for determining the orthodontic treatment may allowcomputational resource efficiency.

Embodiments of the present technology each have at least one of theabove-mentioned object and/or aspects, but do not necessarily have allof them. It should be understood that some aspects of the presenttechnology that have resulted from attempting to attain theabove-mentioned object may not satisfy this object and/or may satisfyother objects not specifically recited herein.

Additional and/or alternative features, aspects and advantages ofembodiments of the present technology will become apparent from thefollowing description, the accompanying drawings and the appendedclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present technology, as well as otheraspects and further features thereof, reference is made to the followingdescription which is to be used in conjunction with the accompanyingdrawings, where:

FIG. 1 depicts a schematic diagram of an orthodontic appliance attachedto five teeth of a plurality of teeth of a subject;

FIG. 2 depicts a schematic diagram of an upper arch form of the subjectof FIG. 1 showing the orthodontic appliance of FIG. 1 attached thereto;

FIG. 3 depicts a schematic diagram of an intermediate phase of theorthodontic treatment including applying the orthodontic appliance ofFIG. 1, in accordance with certain non-limiting embodiments of thepresent technology;

FIG. 4 depicts a schematic diagram of a system for reconstructing 3Drepresentations of root portions associated with the plurality of teethof the subject of FIG. 1 based on associated 3D representations of crownportions for determining the orthodontic treatment, in accordance withcertain embodiments of the present technology;

FIG. 5 depicts a schematic diagram of a computing environment of thesystem of FIG. 4, in accordance with certain embodiments of the presenttechnology;

FIG. 6 depicts a perspective view of a 3D model of the upper arch formand a lower arch form of the subject of FIG. 1, in accordance withcertain non-limiting embodiments of the present technology;

FIG. 7 depicts a portion of the 3D model of FIG. 6 including digitalgarbage to be removed therefrom, in accordance with certain non-limitingembodiments of the present technology;

FIG. 8 depicts a flowchart diagram of a method for generating anaugmented crown 3D representation of the crown portion of a given one ofthe plurality of teeth present in FIG. 1, in accordance with certainnon-limiting embodiments of the present technology;

FIG. 9 depicts a raw crown 3D representation associated with the givenone of the plurality of teeth present in FIG. 1, segmented from the 3Dmodel of FIG. 6, and including some of the digital garbage, inaccordance with certain non-limiting embodiments of the presenttechnology;

FIG. 10 depicts a schematic diagram of a step in the method of FIG. 8executed by the processor of FIG. 5 for identifying and removing thedigital garbage forming part of the raw crown 3D representation of FIG.9 to generate a refined crown 3D representation associated with thegiven one of the plurality of teeth present in FIG. 1, in accordancewith certain non-limiting embodiments of the present technology;

FIG. 11 depicts a schematic diagram of a step in the method of FIG. 8,executed by the processor of FIG. 5, for smoothing, using a Harmonicfunction, a surface of the refined crow 3D representation of FIG. 10 togenerate the augmented crown 3D representation associated with the givenone of the plurality of teeth present in FIG. 1, in accordance withcertain non-limiting embodiments of the present technology;

FIG. 12 depicts the portion of the 3D model of FIG. 7 with the digitalgarbage removed, in accordance with certain non-limiting embodiments ofthe present technology;

FIG. 13 depicts a flowchart diagram of a method for reconstructing, bythe processor of FIG. 5, a root 3D representation of a root portion ofthe given one of the plurality of teeth present in FIG. 1, in accordancewith certain non-limiting embodiments of the present technology.

FIG. 14 depicts the augmented crown 3D representation of FIG. 11 used bythe processor of FIG. 5 for reconstructing the root 3D representation ofthe root portion associated with the given one of the plurality of teethpresent in FIG. 1, in accordance with certain non-limiting embodimentsof the present technology;

FIGS. 15 and 16 depict schematic diagrams of steps of the method of FIG.13, executed by the processor of FIG. 5, for generating a closed curveforming a border between the augmented crown 3D representation of FIG.11 and the root 3D representation, in accordance with certainnon-limiting embodiments of the present technology;

FIGS. 17A and 17B depict schematic diagrams of steps of the method ofFIG. 13, executed by the processor of FIG. 5, for segmenting the closedcurve of FIG. 16 into a plurality of sub-curves used for generating arespective segment of the root 3D representation, in accordance withcertain non-limiting embodiments of the present technology;

FIG. 18 depicts a schematic diagram of a step of the method of FIG. 13,executed by the processor of FIG. 5, for generating the respectivesegment of the root 3D representation, in accordance with certainnon-limiting embodiments of the present technology;

FIG. 19 depicts a schematic diagram of a step of the method of FIG. 13,executed by the processor of FIG. 5, for merging the augmented crown 3Drepresentation of FIG. 11 with the root 3D representation of FIG. 18 forgenerating a tooth 3D representation of the given one of the pluralityof teeth present in FIG. 1, in accordance with certain non-limitingembodiments of the present technology;

FIG. 20 depicts a base parametric model associated with the root portionof given one of the plurality of teeth present in FIG. 1 and a schematicdiagram of smoothing it for augmenting, by the processor of FIG. 5, theroot 3D representation of the FIG. 19, in accordance with certainnon-limiting embodiments of the present technology;

FIG. 21 depicts a schematic diagram of a step of the method of themethod of FIG. 13, executed by the processor of FIG. 5, for merging theaugmented crown 3D representation of FIG. 11 with the augmented root 3Drepresentation of FIG. 20 to generate an augmented tooth 3Drepresentation associated with the given one of the plurality of teethpresent in FIG. 1, in accordance with certain non-limiting embodimentsof the present technology;

FIG. 22 depicts a flowchart diagram of a method for reconstructing acomprehensive gingiva 3D representation of a gingiva associated with theupper arch form of FIG. 2, in accordance with certain non-limitingembodiments of the present technology;

FIG. 23 depicts a portion of the 3D model of FIG. 6 representative of araw 3D representation of the upper arch form of FIG. 2 used, by theprocessor of FIG. 5, to generate the comprehensive gingiva 3Drepresentation associated therewith, in accordance with certainnon-limiting embodiments of the present technology;

FIG. 24 depicts a schematic diagram of a step of the method of FIG. 22,executed by the processor of FIG. 5, for determining a jaw coordinatesystem associated with the raw 3D representation of the upper arch formof FIG. 2, in accordance with certain non-limiting embodiments of thepresent technology;

FIGS. 25 to 28 depict schematic diagrams of steps of the method of FIG.22, executed by the processor of FIG. 5, respectively for generating aplurality of segmentation loops by segmenting 3D tooth representationsof the plurality of teeth present in FIG. 1 from the raw 3Drepresentation of FIG. 23, in accordance with certain non-limitingembodiments of the present technology;

FIG. 29 depicts a schematic diagram of a step of the method of FIG. 22,executed by the processor of FIG. 5, for generating, based on theplurality of segmentation loops of FIG. 28, a primary central curve forgenerating the comprehensive gingiva 3D representation, in accordancewith certain non-limiting embodiments of the present technology;

FIGS. 30 and 31 depict schematic diagrams of steps of the method of FIG.22, executed by the processor of FIG. 5, for generating, based on theprimary central curve of FIG. 29, a border curve of the comprehensivegingiva 3D representation associated with upper arch form of FIG. 2, inaccordance with certain non-limiting embodiments of the presenttechnology;

FIGS. 32A and 32B depict schematic diagrams of steps of the method ofFIG. 22, executed by the processor of FIG. 5, for generating a firstgingiva segment of the comprehensive gingiva 3D representationassociated with upper arch form of FIG. 2, in accordance with certainnon-limiting embodiments of the present technology;

FIG. 33 depicts a schematic diagram of a step of the method of FIG. 22,executed by the processor of FIG. 5, for generating a second gingivasegment of the comprehensive gingiva 3D representation associated withupper arch form of FIG. 2 and additional granulation thereof, inaccordance with certain non-limiting embodiments of the presenttechnology;

FIG. 34 depicts a base gingiva cage representative of the comprehensivegingiva 3D representation associated with upper arch form of FIG. 2having been generated by the processor of FIG. 5, by repeatedly applyingthe steps of FIGS. 32A, 32B, and 33, in accordance with certainnon-limiting embodiments of the present technology;

FIG. 35 depicts the comprehensive gingiva 3D representation of FIG. 34merged with the tooth 3D representations of the plurality of teethpresent in FIG. 1 generated, by the processor of FIG. 5, in accordancewith the methods of FIGS. 8 and 13, forming a comprehensive 3Drepresentation of the upper arch form of FIG. 2, in accordance withcertain non-limiting embodiments of the present technology.

DETAILED DESCRIPTION

Certain aspects and embodiments of the present technology are directedto methods of and systems for reconstructing a comprehensive 3Drepresentation of a gingiva of a subject based on a raw 3Drepresentation thereof. The subject may be receiving, or soon toreceive, an orthodontic treatment. An accurate reconstruction of the 3Drepresentation of the gingiva may allow for a more accurate planning ofthe orthodontic treatment, which can in turn improve overall safety,effectiveness and efficacy of the orthodontic treatment.

Further, it should be expressly understood that, in the context of thepresent specification, the term “orthodontic treatment” is broadlyreferred to as any type of medical intervention aimed at correctingmalocclusions associated with the subject, including surgical andnon-surgical manipulations, such as, but not limited to, using aligners.Further, the orthodontic treatment, as referred to herein, may bedetermined by a professional practitioner in the field of dentistry(such as an orthodontist, a maxillofacial surgeon, for example), orautomatically by a specific software, based on respective image data andinput parameters associated with the subject.

Certain non-limiting embodiments of the present technology minimize,reduce or avoid some of the problems noted in association with the priorart. For example, by implementing certain embodiments of the presenttechnology in respect of reconstructing the comprehensive 3Drepresentation of the gingiva, some or all of the following advantagesmay be obtained: a more efficient and accurate approach to modellingforces imposed on the given tooth, and thus a more accurate modelling ofthe respective movements thereof in the course of the orthodontictreatment. This is achieved in certain non-limiting embodiments of thepresent technology by (1) generating the comprehensive 3D representationof the gingiva only based on raw image data indicative thereof obtainedthrough conventional imaging techniques currently used in orthodontics(such as the intra-oral scanning techniques), without the need forobtaining and processing additional image data associated with thesubject, including, for example, CT and/or MR scans, or panoramicradiographs representative of the root portion of the given tooth; and(2) generating the comprehensive 3D representation of the gingiva, whichis indicative of certain actual anatomical features thereof, such asoverall dimensions thereof, for example, allowing for a more detailedanalysis of movements of the root portions of the subject's teeth in thegingiva; (3) applying textures and colours to the comprehensive 3Drepresentation of the gingiva when outputting it on a screen of acomputer system; and (4) planning material for producing aligners, basedthereon, more efficiently.

Thus, methods and systems provided herein, according to certainnon-limiting embodiments of the present technology, allow achieving ahigher accuracy in planning and predictability of orthodontictreatments, and consequently, resolving malocclusions more efficientlyand effectively whilst using more commonly available imaging techniquesfor generating the image data associated with the subject. For example,the image data used for planning the orthodontic treatment, in somenon-limiting embodiments of the present technology, may include imagesindicative of a surface of the subject's gingiva and respective surfacesof the subject's teeth, such as those obtained with intraoral scans.Images of the roots of the subject's teeth or interdental spaces may notbe required. This may also allow for a faster processing of such imagedata by a processor.

According to some non-limiting embodiments of the present technology,the methods for reconstructing the comprehensive 3D representation ofthe gingiva described herein may be considered as a separate process.However, in other non-limiting embodiments of the present technology,these methods may be part of a more general process of reconstructing acomprehensive 3D representation of a subject's arch form (also referredto herein as an “augmented” 3D representation thereof), which is furtherused for determining the orthodontic treatment, for example, bydisplaying the reconstructed tooth to a practitioner using a display orby using a computer algorithm to generate the treatment plan based onthe reconstructed representation. In these embodiments, thecomprehensive 3D representation of the subject's arch form is generatedbased on a raw 3D representation thereof (that is an unprocessedrepresentation thereof, directly obtained, for example, surface imagingtechniques such as intra-oral scanning techniques, as will be explainedfurther below).

Broadly speaking, according to the non-limiting embodiments of thepresent technology, methods for generating the comprehensive 3Drepresentation of the subject's arch form may include:

-   -   acquiring image data indicative of the raw 3D representation of        the subject's arch form including at least a raw 3D        representation of the crown portion of the given tooth and a raw        3D representation of a gingiva;    -   augmenting the raw 3D representation of the crown portion by        segmentation thereof from respective raw 3D representations of        crown portions of adjacent teeth and that of the gingiva,        thereby generating an augmented 3D representation of the crown        portion of the given tooth;    -   reconstructing, based on the augmented 3D representation of the        crown portion, the 3D representation of the root portion for the        given tooth, thereby generating a 3D representation of the given        tooth; and    -   augmenting, based at least on the 3D representation of the crown        portion, the raw 3D representation of the gingiva, thereby        generating a comprehensive 3D representation thereof (which is        the object of the present document).

As it may become apparent, the last step may further include merging the3D representation of the given tooth with the comprehensive 3Drepresentation of the gingiva, whereby the comprehensive 3Drepresentation of the subject's arch form may be generated. It should bealso noted that the order of steps listed above can be changed withoutdeparting from the scope of the non-limiting embodiments of the presenttechnology.

Thus, the description of the non-limiting embodiments of the presenttechnology directed to reconstruction of the comprehensive 3Drepresentation of the gingiva will be provided in concert withdescription of the above-listed steps for the generating thecomprehensive 3D representation of the subject's arch form.

Orthodontic Treatment

Referring initially to FIGS. 1 and 2, there is depicted an exampleorthodontic appliance 10 as part of the orthodontic treatment, to whichcertain aspects and embodiments of the present technology can beapplied. Generally speaking, the orthodontic appliance 10 comprisesbrackets 12 and an archwire 14. The archwire 14 is made of a shapememory alloy such as Nitinol™, but can also be made of any other shapememory alloy or material having certain elasticity properties. Thebrackets 12 are respectively provided on some of upper teeth 16(depicted individually as 11, 13, 15, 17, and 19), and the archwire 14extends between, and is connected to each of the brackets 12. In thedepicted embodiments of FIG. 1, the orthodontic treatment is aimed atmisalignment of the tooth 15; hence the orthodontic appliance 10 isconfigured to cause the tooth 15 to move in a predetermined direction(such as downwardly) for alignment thereof with neighbouring ones of theupper teeth 16, that is, teeth 11, 13, 17, and 19.

As it can be appreciated from FIG. 1, the tooth 15 includes a crownportion 26 and a root portion 28. The archwire 14 imposes a given force,caused by bends 18, on the tooth 15 at a respective one of the brackets12 having been installed on the crown portion 26. Thus, due to the shapememory effect of the archwire 14, the tooth 15 will gradually move to analigned position relative to the other one of the upper teeth 16.

With reference to FIG. 2, as one non-limiting example, the orthodonticappliance 10 has been applied to all the upper teeth 16 of an upper archform 20 of the subject, with the brackets 12 being attached to aninternal surface 22 of the upper teeth 16. However, it should be notedthat, in another non-limiting example, the orthodontic appliance 10 maybe configured to be installed on an external surface 24 of the upperteeth 16.

It is contemplated that, according to some non-limiting embodiments ofthe present technology, the orthodontic appliance 10 may compriseorthodontic appliances of different types, shapes, sizes andconfigurations, such as, without limitation, multi-strand wires, strips,retainers, and plates. Furthermore, the bends 18 in the archwire 14 maycomprise rounded corners or loops. It will also be appreciated that theorthodontic appliance 10 may be used for treating any type of teethmisalignment or malocclusion, including but not limited to closing gaps(“space closure”), creating/widening gaps, tooth rotation, toothintrusion/extrusion, and translation, to name a few.

It is contemplated that, before installing the orthodontic appliance 10onto the upper teeth 16 for the alignment of the tooth 15, movementsthereof, in the course of the orthodontic treatment, should be modelledto ensure that the tooth 15 will eventually reach the aligned positionover an expected period. To that end, image data indicative of crownportions (such as the crown portion 26 of the tooth 15) of the upperteeth 16 may be used to model the given force to be applied onto thetooth 15, which may include, without being limited to: a magnitude ofthe given force, a direction thereof, and an application point thereofwithin the crown portion 26. Accordingly, based on the image dataindicative of the crown portions, the modelling may, for example, allowavoiding collisions between the crown portion 26 of the tooth 15 withany one of those teeth of the upper teeth 16 adjacent thereto.

However, in certain cases, the modelling of the tooth movements may beconducted to prevent other undesired effects of the orthodontictreatment. For example, the modelling may allow ensuring that thecurrent orthodontic treatment would not cause damage to any of the upperteeth 16 at the level of their root portions, as well as to otherstructures associated therewith, such as tissues of an upper gingiva(such as an upper gingiva 36 depicted in FIG. 6), those of a maxillaryalveolar bone (not depicted), proximal nerve pathways and blood vessels(not depicted), and the like. Further, when modelling tooth movements,considerations can be made in respect of overall comfort of theorthodontic treatment for the subject, on which his or her tolerance andadherence to the orthodontic treatment may depend.

For example, with reference to FIG. 3, there is depicted a schematicdiagram of a phase of the orthodontic treatment based on applying theorthodontic appliance 10 to the upper teeth 16, in accordance withcertain non-limiting embodiments of the present technology. The depictedphase may be an intermediate phase or an initial phase, for example.

As it can be appreciated, at the phase depicted in FIG. 3, the rootportion 28 of the tooth 15, in the course of the movement thereoftowards the aligned position, collides with a root portion (notseparately labelled) of the tooth 17 adjacent thereto, thereby forming acollision area 30. Accordingly, the collision area 30 may be associatedwith undesired effects, such as damage of one of the tooth 15 and thetooth 17, or discomfort (pain, for example) caused to the subject.

In another example (not depicted), the collision may occur between thecrown portion 26 of the tooth 15 and a crown portion (not separatelylabelled) of the tooth 17, which may result in damage (such as chippingor cracks) to at least one of the crown portion 26 and the crownportion, or also pain to the subject from pressure therebetween.

In yet another example (not depicted), the root portion 28 may deviatein another direction causing damage to the upper gingiva 36, which mayresult in the root portion 28 protruding through the upper gingiva 36causing to the subject, for example, an aesthetic defect or, again,discomfort associated with pain from using the orthodontic appliance 10.

Overall, the image data solely indicative of the crown portion 26 may beinsufficient for a comprehensive analysis of the movements anddetermining intermediate positions of the tooth 15, as a whole, duringthe orthodontic treatment, which may hence require image data indicativeof the root portion 28 thereof and that indicative of the upper gingiva36, for example. Such comprehensive analysis may allow for a moreaccurate planning of the orthodontic treatment of the subject, aimed atmitigating the risks of at least some of the undesired effects thereof.How the raw image data indicative of the crown portion 26 may be usedfor generating the augmented 3D representation thereof will be describedbelow with reference to FIGS. 7 to 12. Further, how the augmented 3Drepresentation of the crown portion 26 may be used for generating imagedata indicative of the root portion 28 will be described further belowwith reference to FIGS. 13 to 21. Finally, how the so generated imagedata may be used, along with the raw 3D representation of the uppergingiva 36, to generate the comprehensive 3D model thereof will bedescribed with reference to FIGS. 22 to 35.

System

Referring to FIGS. 4 and 5, there is depicted a schematic diagram of asystem 400 suitable for determining root reconstructions such as fordetermining the orthodontic treatment for the subject, in accordancewith certain non-limiting embodiments of the present technology.

It is to be expressly understood that the system 400 as depicted ismerely an illustrative implementation of the present technology. Thus,the description thereof that follows is intended to be only adescription of illustrative examples of the present technology. Thisdescription is not intended to define the scope or set forth the boundsof the present technology. In some cases, what is believed to be helpfulexamples of modifications to the system 400 may also be set forth below.This is done merely as an aid to understanding, and, again, not todefine the scope or set forth the bounds of the present technology.These modifications are not an exhaustive list, and, as a person skilledin the art would understand, other modifications are likely possible.Further, where this has not been done (i.e., where no examples ofmodifications have been set forth), it should not be interpreted that nomodifications are possible and/or that what is described is the solemanner of implementing that element of the present technology. As aperson skilled in the art would understand, this is likely not the case.In addition, it is to be understood that the system 400 may provide incertain instances simple implementations of the present technology, andthat where such is the case they have been presented in this manner asan aid to understanding. As persons skilled in the art would furtherunderstand, various implementations of the present technology may be ofa greater complexity.

In certain non-limiting embodiments of the present technology, thesystem 400 of FIG. 4 comprises a computer system 410. The computersystem 410 may be configured, by pre-stored program instructions, togenerate, based on image data associated with the subject, acomprehensive arch form 3D representation of the upper arch form 20including: (i) augmented crown 3D representations, (ii) root 3Drepresentations for the upper teeth 16 thereby generating respectivetooth 3D representations, and (iii) a comprehensive gingiva 3Drepresentation of the upper gingiva 36, according to certainnon-limiting embodiments of the present technology. In some non-limitingembodiments of the present technology, the computer system 410 mayfurther be configured to determine, based at least on one of therespective tooth 3D representations and the comprehensive gingiva 3Drepresentation, the orthodontic treatment for the subject, as will bedescribed further It should be noted that in various non-limitingembodiments of the present technology, the computer system 410 may beconfigured to execute the steps (i), (ii), and (iii) separately and/orindependently. Further, the order of these steps may be changed withoutdeparting from the scope of the present technology.

To that end, in some non-limiting embodiments of the present technology,the computer system 410 is configured to receive image data pertainingto the subject or to a given orthodontic treatment. For example, thecomputer system 410 may be configured to process the received image datato generate the comprehensive 3D representation of the subject's archform. According to some non-limiting embodiments of the presenttechnology, the computer system 410 may receive the image data via localinput/output interface (such as USB, as an example, not separatelydepicted). In other non-limiting embodiments of the present technology,the computer system 410 may be configured to receive the image data overa communication network 425, to which the computer system 410 iscommunicatively coupled.

In some non-limiting embodiments of the present technology, thecommunication network 425 is the Internet and/or an Intranet. Multipleembodiments of the communication network may be envisioned and willbecome apparent to the person skilled in the art of the presenttechnology. Further, how a communication link between the computersystem 410 and the communication network 425 is implemented will depend,inter alia, on how the computer system 410 is implemented, and mayinclude, but is not limited to, a wire-based communication link and awireless communication link (such as a Wi-Fi communication network link,a 3G/4G communication network link, and the like).

It should be noted that the computer system 410 can be configured forreceiving the image data from a vast range of devices. Some of suchdevices can be used for capturing and/or processing data pertaining tomaxillofacial and/or cranial anatomy of the subject. In certainembodiments, the image data received from such devices is indicative ofproperties of anatomical structures of the subject, including: teeth,intraoral mucosa, maxilla, mandible, temporomandibular joint, and nervepathways, among other structures. In some non-limiting embodiments ofthe present technology, at least some of the image data is indicative ofproperties of external portions of the anatomical structures, forexample dimensions of a gingival sulcus, and dimensions of an externalportion of a tooth (e.g., a crown of the tooth) extending outwardly ofthe gingival sulcus. In some embodiments, the image data is indicativeof properties of internal portions of the anatomical structures, forexample volumetric properties of bone surrounding an internal portion ofthe tooth (e.g., a root of the tooth) extending inwardly of the gingivalsulcus. Under certain circumstances, such volumetric properties may beindicative of periodontal anomalies which may be factored into anorthodontic treatment plan. In some non-limiting embodiments of thepresent technology, the image data includes cephalometric imagedatasets. In some embodiments, the image data includes datasetsgenerally intended for the practice of endodontics. In some embodiments,the image data includes datasets generally intended for the practice ofperiodontics.

In alternative non-limiting embodiments of the present technology, thecomputer system 410 may be configured to receive the image dataassociated with the subject directly from an imaging device 430communicatively coupled thereto. Broadly speaking the imaging device 430may be configured (for example, by a processor 550 depicted in FIG. 5)to capture and/or process the image data of the upper teeth 16 and theperiodontium (not depicted) of the subject. In certain non-limitingembodiments of the present technology, the image data may include, forexample, one or more of: (1) images of external surfaces of respectivecrown portions (such as the crown portion 26 of the tooth 15) of theupper teeth 16, (2) images of an external surface of the periodontiumincluding those of the upper gingiva (not depicted), the alveolarmaxillary bone (not depicted), and images of superficial blood vesselsand nerve pathways associated with the upper teeth 16; and (3) images ofan oral region. By doing so, the imaging device 430 may be configured,for example, to capture image data of the upper arch form 20 of thesubject. In another example, the imaging device may also be configuredto capture and/or process image data of a lower arch form (such as thelower arch form 21 depicted in FIG. 6) associated with the subjectwithout departing from the scope of the present technology. It should benoted that the image data may include two-dimensional (2D) data and/orthree-dimensional data (3D). Further, in certain non-limitingembodiments of the present technology, the image data includes 2D data,from which 3D data may be derived, and vice versa.

In some non-limiting embodiments of the present technology, the imagingdevice 430 may comprise an intra-oral scanner enabling to capture directoptical impressions of the upper arch form 20 of the subject.

In a specific non-limiting example, the intraoral scanner can be of oneof the types available from MEDIT, corp. of 23 Goryeodae-ro 22-gil,Seongbuk-gu, Seoul, South Korea. It should be expressly understood thatthe intraoral scanner can be implemented in any other suitableequipment.

In other non-limiting embodiments of the present technology, the imagingdevice 430 may comprise a desktop scanner enabling to digitize a moldrepresenting the upper arch form 20. In this regard, the mold may havebeen obtained via dental impression using a material (such as a polymer,e.g. polyvinyl-siloxane) having been imprinted with the shape of theintraoral anatomy it has been applied to. In the dental impression, aflowable mixture (i.e., dental stone powder mixed with a liquid incertain proportions) may be flowed such that it may, once dried andhardened, form the replica.

In a specific non-limiting example, the desktop scanner can be of one ofthe types available from Dental Wings, Inc. of 2251, ave Letourneux,Montreal (QC), Canada, H1V 2N9. It should be expressly understood thatthe desktop scanner can be implemented in any other suitable equipment.

Further, it is contemplated that the computer system 410 may beconfigured for processing of the received image data. The resultingimage data of the upper arch form 20 received by the computer system 410is typically structured as a binary file or an ASCII file, may bediscretized in various ways (e.g., point clouds, polygonal meshes,pixels, voxels, implicitly defined geometric shapes), and may beformatted in a vast range of file formats (e.g., STL, OBJ, PLY, DICOM,and various software-specific, proprietary formats). Any image data fileformat is included within the scope of the present technology. Forimplementing functions described above, the computer system 410 mayfurther comprise a corresponding computing environment.

With reference to FIG. 5, there is depicted a schematic diagram of acomputing environment 540 suitable for use with some implementations ofthe present technology. The computing environment 540 comprises varioushardware components including one or more single or multi-coreprocessors collectively represented by the processor 550, a solid-statedrive 560, a random access memory 570 and an input/output interface 580.Communication between the various components of the computingenvironment 540 may be enabled by one or more internal and/or externalbuses 590 (e.g. a PCI bus, universal serial bus, IEEE 1394 “Firewire”bus, SCSI bus, Serial-ATA bus, ARINC bus, etc.), to which the varioushardware components are electronically coupled.

The input/output interface 580 allows enabling networking capabilitiessuch as wire or wireless access. As an example, the input/outputinterface 580 comprises a networking interface such as, but not limitedto, a network port, a network socket, a network interface controller andthe like. Multiple examples of how the networking interface may beimplemented will become apparent to the person skilled in the art of thepresent technology. For example, but without being limiting, theinput/output interface 580 may implement specific physical layer anddata link layer standard such as Ethernet™, Fibre Channel, Wi-Fi™ orToken Ring. The specific physical layer and the data link layer mayprovide a base for a full network protocol stack, allowing communicationamong small groups of computers on the same local area network (LAN) andlarge-scale network communications through routable protocols, such asInternet Protocol (IP).

According to implementations of the present technology, the solid-statedrive 560 stores program instructions suitable for being loaded into therandom access memory 570 and executed by the processor 550, according tocertain aspects and embodiments of the present technology. For example,the program instructions may be part of a library or an application.

In some non-limiting embodiments of the present technology, thecomputing environment 540 is implemented in a generic computer systemwhich is a conventional computer (i.e. an “off the shelf” genericcomputer system). The generic computer system may be a desktopcomputer/personal computer, but may also be any other type of electronicdevice such as, but not limited to, a laptop, a mobile device, a smartphone, a tablet device, or a server.

As persons skilled in the art of the present technology may appreciate,multiple variations as to how the computing environment 540 can beimplemented may be envisioned without departing from the scope of thepresent technology.

Referring back to FIG. 4, the computer system 410 has at least oneinterface device 420 for providing an input or an output to a user ofthe system 400, the interface device 420 being in communication with theinput/output interface 580. In the embodiment of FIG. 4, the interfacedevice is a screen 422. In other non-limiting embodiments of the presenttechnology, the interface device 420 may be a monitor, a speaker, aprinter or any other device for providing an output in any form such asan image form, a written form, a printed form, a verbal form, a 3D modelform, or the like.

In the depicted embodiments of FIG. 4, the interface device 420 alsocomprises a keyboard 424 and a mouse 426 for receiving input from theuser of the system 400. Other interface devices 420 for providing aninput to the computer system 410 can include, without limitation, a USBport, a microphone, a camera or the like.

The computer system 410 may be connected to other users, such as throughtheir respective clinics, through a server (not depicted). The computersystem 410 may also be connected to stock management or client softwarewhich could be updated with stock when the orthodontic treatment hasbeen determined and/or schedule appointments or follow-ups with clients,for example.

Image Data

As previously alluded to, according to the non-limiting embodiments ofthe present technology, the processor 550 may be configured to: (1)receive the image data associated with the subject's teeth (such as theupper teeth 16); and (2) based on the received image data, determine,for each of the upper teeth 16, the orthodontic treatment for thesubject. For example, based on the received data, the processor 550 maybe configured to determine tooth movements of the tooth 15 towards thealigned position thereof within the other ones of the upper teeth 16, asdescribed above with reference to FIGS. 1 to 3.

According to some non-limiting embodiments of the present technology,having received the image data, the processor 550 may be configured togenerate 3D models of arch forms of the subject.

With reference to FIG. 6, there is depicted a perspective view of a 3Dmodel 600 representing a current configuration of the upper arch form 20(also referred to herein as “maxillary arch form”) and the lower archform 21 (also referred to herein as “mandibular arch form”) of thesubject, in accordance with the non-limiting embodiments of the presenttechnology.

According to the non-limiting embodiments of the present technology, theupper arch form 20 comprises the upper teeth 16 (also referred to hereinas “maxillary teeth”) and the upper gingiva 36, and the lower arch form21 comprises lower teeth 27 (also referred to herein as “mandibularteeth”) and a lower gingiva 37. As it can be appreciated, the upperteeth 16 and the lower teeth 27 are represented, in the 3D model 600, byrespective crown portions associated therewith, such as the crownportion 26 of the tooth 15.

It should be expressly understood that, although the description hereinbelow will be given in respect of the upper arch form 20 of the subject(and associated therewith the upper teeth 16 and the upper gingiva 36)for the sake of clarity and simplicity thereof, and in no way as alimitation, the non-limiting embodiments of the present technology canalso apply to the lower teeth 27 with certain alterations, which will beexplicitly indicated below where necessary.

Further, according to some non-limiting embodiments of the presenttechnology, in order to determine the orthodontic treatment, theprocessor 550 may be configured to isolate, in the 3D model 600, a 3Drepresentation of the crown portion 26 (such as an augmented crown 3Drepresentation 1020 depicted in FIG. 10, for example) from 3Drepresentations of crown portions associated with other ones of theupper teeth 16, and from that of the upper gingiva 36. Further, theprocessor 550 may be configured to reconstruct, based on the 3Drepresentation of the crown portion 26, a 3D representation of the rootportion 28 (such as a root 3D representation 1620 depicted in FIG. 17,for example), thereby generating a complete 3D representation of thetooth 15 (such as a tooth 3D representation 1720 depicted in FIG. 17,for example), which complete 3D representation may be used fordetermining the orthodontic treatment.

However, the so generated 3D model 600 may not be accuratelyrepresentative of actual configuration of at least some of the upperteeth 16. For example, the imaging device 430 of FIG. 4 may not be ableto capture interdental spaces between each of the teeth accurately, forexample, due to an inability thereof to reliably receive light havingbeen reflected off the interdental spaces. This may result in theprocessor 550 generating the 3D model 600 including image artefacts(also known as “digital garbage”) instead of data indicative of actualinterdental spaces between the teeth of the subject, which may furtherrender the 3D model 600 unreliable for further processing.

With reference to FIG. 7, there is depicted a magnified view of the 3Dmodel 600 representing a portion of the upper arch form 20 with some ofthe upper teeth 16 including image artefacts 700 instead of respectiverepresentations of interdental spaces therebetween, in accordance withcertain non-limiting embodiments of the present technology.

In the context of the present specification, the term “image artefacts”of an image (such as the 3D model 600) representative of a real object(such as the upper arch form 20) broadly refers to portions of the imageforming no part of the real object and generated, for example, due toimperfection of technical means (such as the imaging device 430) usedfor taking the image. As such, for a more accurate representation of thereal object, the image artefacts need to be identified and removed fromthe image.

As it can be appreciated from FIG. 7, the image artefacts 700 representanomalies in representing the upper teeth 16 and the upper gingiva 36forming no part of the actual configuration thereof. Therefore, the 3Dmodel 600 including the image artefacts 700 may not enable thegeneration of the 3D representation of the crown portion 26 indicativeof actual surface thereof at a desired level of detail, providinginstead a raw 3D representation thereof (such as a raw crown 3Drepresentation 800 depicted in FIG. 8). This may, in turn, result in aninaccurate 3D representation of the root portion 28.

Thus, in certain non-limiting embodiments of the present technology, theprocessor 550 may be configured to execute a method 100 for identifying,in the 3D model 600, the image artefacts 700 and effectively eliminatingthem, thereby segmenting individual 3D representations of crown portionsof the upper teeth 16 from each other and from that of the upper gingiva36. By doing so, the processor 550 may be configured to restore, in the3D model 600, an actual contour of a respective surface of each of thecrown portions, thereby generating an augmented crown 3D representation(such as the augmented crown 3D representation depicted in FIG. 11) ofthe crown portion 26 of the tooth 15. How these non-limiting embodimentscan be implemented will be described with reference to FIGS. 9 to 12.

Automatic Tooth Segmentation

With reference to FIG. 8, there is depicted a flowchart diagram of themethod 100 for generating the augmented crown 3D representation 1020 ofthe crown portion 26. According to certain non-limiting embodiments ofthe present technology, the method 100 can be executed by the processor550 of the computer system 410.

Step 102: Acquiring a Raw 3D Representation of an Arch Form of thePatient, the Arch Form Comprising a Gingiva and at Least One Tooth ofthe Patient

The method 100 commences at step 102 with acquiring a raw 3Drepresentation of the upper arch form 20, such as that forming part ofthe 3D model 600, the process of receiving which is describedhereinabove with reference to FIGS. 6 and 7.

Further, with reference to FIG. 9, there is depicted the raw crown 3Drepresentation 800 of the crown portion 26, in accordance with certainnon-limiting embodiments of the present technology. For example, in somenon-limiting embodiments of the present technology, the processor 550may be configured to isolate, from the 3D model 600, the raw crown 3Drepresentation 800 of the crown portion 26 based on reference dataassociated with the tooth 15. The reference data may be based onhistoric data of a number of subjects, such as average maximum possibledimensions of crown portions. In alternative non-limiting embodiments ofthe present technology, to generate the raw crown 3D representation 800,the processor 550 may have been configured to use algorithms foranalyzing changes of curvature within the 3D model 600.

In some non-limiting embodiments of the present technology, theprocessor 550 may be configured to generate the raw crown 3Drepresentation 800 comprising a plurality of mesh elements 806. Althoughin the depicted embodiments of FIG. 9 each of the plurality of meshelements 806 is a triangular mesh element, it should be expresslyunderstood that in other non-limiting embodiments of the presenttechnology, the plurality of mesh elements 806 may be represented byquadrilateral mesh elements, convex polygonal mesh elements, or evenconcave polygonal mesh elements, as an example, without departing fromthe scope of the present technology.

As can be appreciated from FIG. 9, the raw crown 3D representation 800includes the image artefacts 700, which may impede the accuratedetermination of actual boundaries of the crown portion 26 of the tooth15. Thus, the processor 550 may be configured to: (1) identify the imageartefacts 700 in the raw crown 3D representation 800 of the crownportion 26; (2) remove image artefacts 700 therefrom; and (3) smooth theresulting surface thereof, thereby generating an augmented crown 3Drepresentation of the crown portion 26. The augmented crown 3Drepresentation may be further used to determine the orthodontictreatment for the subject.

Certain non-limiting embodiments of the present technology have beendeveloped based on developers' appreciation that the image artefacts 700may be identified based on a pre-defined portion of the raw crown 3Drepresentation 800 known to accurately represent a respective actualportion of the crown portion 26 of the tooth 15—such as a definedportion 802 thereof as depicted in FIG. 9. To that end, the definedportion 802 of the raw crown 3D representation 800 may be used, by theprocessor 550, to determine overall smoothness of a surface of theaugmented crown 3D representation 1020 of the crown portion 26, therebyidentifying: (1) portions of the raw crown 3D representation 800 thatcorrespond to the surface of the augmented crown 3D representation 1020,and that should thus be included therein; and (2) portions of the rawcrown 3D representation 800 that do not correspond to the surface of theaugmented crown 3D representation 1020. According to some non-limitingembodiments of the present technology, the processor 550 may further beconfigured to identify the latter as portions indicative of the imageartefacts 700, which should be removed from the raw crown 3Drepresentation 800.

In some non-limiting embodiments of the present technology, theprocessor 550 may be configured to determine the defined portion 802based on a predetermined horizontal distance from at least one verticaledge of the raw crown 3D representation 800—such as a vertical edge808—along a horizontal axis (not depicted) associated therewith.

In some non-limiting embodiments of the present technology, thehorizontal axis associated with the raw crown 3D representation 800 maybe defined, for example, based on a transverse anatomical plane (notseparately depicted) associated with the subject's skull. In othernon-limiting embodiments of the present technology, the horizontal axismay be defined as an axis extending between a most distant distal vertex(not depicted) of the plurality of mesh elements 806 and a most mesialvertex (not depicted) of the plurality of mesh elements 806, which mayhave been predetermined within the defined portion 802 of the raw crown3D representation 800. Further, based on the so defined horizontal axis,the processor 550 may be configured to generate a coordinate system 805for the raw crown 3D representation 800 of the crown portion 26.

According to some non-limiting embodiments of the present technology, todetermine the predetermined horizontal distance, the processor 550 maybe configured to execute (or otherwise have access to) an erosionfunction. In the context of the present specification, the term“erosion” broadly refers to morphological image processing developed inthe field of mathematical morphology, and denotes a function configuredto remove structural elements (such as some of the plurality of meshelements 806) from boundaries of an image (such as the raw crown 3Drepresentation 800 of the crown portion 26) based on a predeterminedstructuring element comprising a predetermined number of the structuralelements, on whose configuration the output of the erosion functiondepends. In this regard, the configuration of the structuring elementmay include a size and a shape thereof, and certain image parametersassociated with the structural elements of the image, such as lightintensity or colour, for example. Accordingly, the structuring elementcan be said to move within the image akin to a sliding window, removingportions thereof that do not correspond to the configuration of thestructuring element. By so doing, the erosion function may be configuredto isolate only a substantive portion of the image.

Thus, broadly speaking, a value of the predetermined horizontaldistance, determined by the processor 550 based on the erosion function,may be variable along the vertical edge 808 of the raw crown 3Drepresentation 800. Thus, by applying the predetermined horizontaldistance, the processor 550 may be configured to identify a plurality ofconstrained mesh elements 810 representing the defined portion 802, andthe remainder—as a plurality of unconstrained mesh elements 812representing an undefined portion 804 of the raw 3D representation 800of the crown portion.

The method 100 hence advances to step 104.

Step 104: Generating a Set of Confirmed Constrained Vertices, Includingthe Constrained Vertices Associated with the Defined Portion, forProviding the Augmented 3D Representation of the Given Tooth

At step 104, according to certain non-limiting embodiments of thepresent technology, having identified the defined portion 802 and theundefined portion 804 of the raw crown 3D representation 800, theprocessor 550 may be configured to identify the image artefacts 700 inthe raw crown 3D representation 800. To that end, the processor 550 maybe configured to use the plurality of constrained mesh elements 810 fordetermining if a given adjacent one of the plurality of unconstrainedmesh elements 812 should be re-identified as one of the plurality ofconstrained mesh elements 810 and transferred thereto, or else beidentified as forming part of the image artefacts 700 and removed fromthe raw crown 3D representation 800. By so doing, the processor 550 maybe configured to generate a plurality of confirmed constrained meshelements (such as the plurality of confirmed constrained mesh elements920 depicted in FIGS. 10 and 11) representing the augmented crown 3Drepresentation 1020 of the crown portion 26, as will be explained ingreater detail below.

In some non-limiting embodiments of the present technology, theprocessor 550 may be configured to determine if the given one of theplurality of unconstrained mesh elements 812 should be included in theplurality of confirmed constrained mesh elements 920 based on analyzinga spatial position thereof relative to a respective one of the pluralityof constrained mesh elements 810 within the coordinate system 805.

With reference to FIG. 10, there is depicted a schematic diagram ofexecuting, by the processor 550, step 104 for identifying each one ofthe plurality of unconstrained mesh elements 812 as being representativeof the crown portion 26 or of the image artefacts 700, therebygenerating the plurality of confirmed constrained mesh elements 920, inaccordance with certain non-limiting embodiments of the presenttechnology.

According to certain non-limiting embodiments of the present technology,the processor 550 may be configured to determine if an unconstrainedmesh element 903 is to be included in the plurality of confirmedconstrained mesh elements 920 or to be considered part of the imageartefacts 700 by determining an angular position thereof relative to afirst constrained mesh element 902 adjacent thereto. Thus, the processor550 may be configured to include, in the plurality of confirmedconstrained mesh elements 920, those, from the plurality ofunconstrained mesh elements 812, having certain degree of smoothnessrelative to the plurality of constrained mesh elements 810.

To that end, the processor 550 may be configured to first determine, ateach vertex of each one of the plurality of mesh elements 806, anassociated vertex normal vector. Thus, by determining angular differencebetween a pair of immediately adjacent vertex normal vectors defined atrespective vertices of two adjacent mesh elements of the plurality ofmesh elements 806, discontinuity of smoothness between the two adjacentmesh elements may be detected, as will be explained below.

It should be expressly understood that how the processor 550 can beconfigured to determine the associated vertex normal vector is notlimited, and, typically, may include analyzing spatial positions ofassociated edges of a respective one of the plurality of mesh elements806, face normal vectors associated therewith (not depicted), and thelike, within the coordinate system 805. In this regard, as it will beappreciated by one skilled in the art, the processor 550 may beconfigured to apply one of the following techniques to determine theassociated vertex normal vector: a mean weighted equality algorithm, amean weighted by angle algorithm, a mean weighted by sine and edgelength reciprocal algorithm, a mean weighted by areas of adjacent meshelements, and the like. Details of implementation of some of thesealgorithms may be obtained, for example, from an article titled “AComparison of Algorithms for Vertex Normal Computation” by ShuangshuangJin, Robert R. Lewis, David West, and published by Washington StateUniversity, the content of which is incorporated herein by reference inits entirety.

Thus, with continued reference to FIG. 10, the first constrained meshelement 902 may be represented by a plurality of constrained vertices910, at each of which the processor 550 may be configured to determine arespective one of a plurality of constrained vertex normal vectors 912.By the same token, the unconstrained mesh element 903 may be representedby a plurality of unconstrained vertices 911, for each of which theprocessor 550 may be configured to determine a respective one of aplurality of unconstrained vertex normal vectors 913.

Further, as can be appreciated from FIG. 10, a given constrained vertex904 is adjacent to a given unconstrained vertex 905 within the pluralityof mesh elements 806. In turn, the given constrained vertex 904 isassociated with a given constrained vertex normal vector 914, and thegiven unconstrained vertex 905 is associated with a given unconstrainedvertex normal vector 915. Thus, by determining an angular difference916, 0, within the coordinate system 805, between the given constrainedvertex normal vector 914 and the unconstrained vertex normal vector 915,the processor 550 may be configured to determine the degree ofsmoothness between the first constrained mesh element 902 and theunconstrained mesh element 903.

For example, the processor 550 may be configured to compare the angulardifference 916 to a predetermined angular difference threshold value,such that: (1) in response to the angular difference 916 being equal toor below the predetermined angular difference threshold value, theprocessor 550 may be configured to identify the unconstrained meshelement 903 as being smooth with respect to the first constrained meshelement 902, thereby including the unconstrained mesh element in theplurality of confirmed constrained mesh elements 920; or (2) in responseto the angular difference 916 being greater than the predeterminedangular difference threshold value, the processor 550 may further beconfigured to identify the given unconstrained vertex 905 as a point ofdiscontinuity of smoothness between the first constrained mesh element902 and the unconstrained mesh element 903, thereby rejecting it fromthe plurality of confirmed constrained mesh elements 920. Accordingly,in the latter case, the rejecting the unconstrained mesh element 903from inclusion thereof in the plurality of confirmed constrained meshelements 920 would result in forming a gap in the augmented crown 3Drepresentation 1020 of the crown portion 26.

In some non-limiting embodiments of the present technology, thepredetermined angular difference threshold value can be determined basedon experimental data. For example, the predetermined angular differencethreshold value can be determined based on a particular configuration ofthe crown portion 26 and/or a desired level of smoothness of theaugmented crown 3D representation 1020 thereof. In a specific example,the predetermined angular difference threshold value may be selectedfrom an interval from 0 to 10 degrees, or from 10 to 20 degrees.

As the given unconstrained vertex 905 may be adjacent to otherconstrained vertices (not separately labelled), such as those,respectively defining a second constrained mesh element 906 and a thirdconstrained mesh element 908, in other non-limiting embodiments of thepresent technology, the processor 550 may be configured to examine eachof constrained vertex normal vectors associated therewith with respectto the given unconstrained vertex normal vector 915 as describedhereinabove. To that end, the processor 550 may be configured to includethe unconstrained mesh element 903 in the plurality of confirmedconstrained mesh elements 920 based on a number of the associatedconstrained vertex normal vectors, with which a respective angulardifference between the given unconstrained vertex normal vector 915 isequal to or below than the predetermined angular difference thresholdvalue. For example, the processor 550 may be configured to allow theunconstrained mesh element 903 if at least two adjacent constrainedvertex normal vectors associated with the first constrained mesh element902, the second constrained mesh element 906, and the third constrainedmesh element 908 form a respective angular difference with the givenunconstrained vertex normal vector 915 which is equal to or below thepredetermined angular difference threshold value. Conversely, theprocessor 550 may be configured to reject the unconstrained mesh element903 from inclusion in the plurality of confirmed constrained meshelements 920 if the at least two adjacent constrained vertex normalvectors associated with the first constrained mesh element 902, thesecond constrained mesh element 906, and the third constrained meshelement 908 form the respective angular difference with the givenunconstrained vertex normal vector 915 which is greater than thepredetermined angular difference threshold value.

In yet other non-limiting embodiments of the present technology, to makesuch determination, the processor 550 may further be configured toconsider a maximum one of respective angular differences formed by oneof the first constrained mesh element 902, the second constrained meshelement 906, and the third constrained mesh element 908 with the givenunconstrained vertex normal vector 915, as an example.

In certain non-limiting embodiments of the present technology, theprocessor 550 may be configured to determine if the unconstrained meshelement 903 is to be included in the plurality of confirmed constrainedmesh elements for further processing or rejected by applying anExpectation Maximization (EM) algorithm. To that end, the processor 550may be configured to predetermine initial statistical parameters, suchas means and variances, for example, of respective distributions ofconstrained vertices within the plurality of constrained mesh elements810 and unconstrained vertices within the plurality of unconstrainedmesh elements 812. In specific non-limiting embodiments of the presenttechnology, the processor 550 may be configured to predetermine theinitial statistical parameters by using a Machine Learning Algorithm(MLA) having been specifically trained for determining statisticalparameters of distribution of vertices within associated pluralities ofmesh elements.

In this regard, by using the EM algorithm, the processor 550 may beconfigured to determine a likelihood value that the given unconstrainedvertex 905 and the unconstrained mesh element 903 defined thereby formspart of either (i) the augmented crown 3D representation 1020 of thecrown portion 26, and thus should be included in the plurality ofconfirmed constrained mesh elements 920, or (ii) the image artefacts700, and thus should be rejected.

Thus, according to certain non-limiting embodiments of the presenttechnology, iteratively identifying, from the plurality of unconstrainedmesh elements 812, those associated with the image artefacts 700 andrejecting them, the processor 550 may be configured to generate arefined crown 3D representation of the crown portion 26.

With reference to FIG. 11, there is depicted a schematic diagram of arefined crown 3D representation 1000 of the crown portion 26 generatedby excluding the image artefacts 700 from the raw crown 3Drepresentation 800, in accordance with certain non-limiting embodimentsof the present technology.

As mentioned earlier with reference to FIGS. 9 and 10, determining, bythe processor 550, the plurality of confirmed constrained mesh elements920 representative of the refined crown 3D representation 1000 byrejecting therefrom those of the plurality of unconstrained meshelements 812 representative of the image artefacts 700, may form gaps inthe refined crown 3D representation 1000.

Thus, with reference to FIG. 11, according to certain non-limitingembodiments of the present technology, the processor 550 may beconfigured to smooth a surface of the refined crown 3D representation1000 filling in gaps 1004, thereby generating the augmented crown 3Drepresentation 1020 of the crown portion 26.

To that end, according to specific non-limiting embodiments of thepresent technology, the processor 550 may be configured to apply one ormore Harmonic functions 1008 to the refined crown 3D representation 1000of the crown portion 26, thereby restoring a smooth surface 1010 withinthe gaps 1004.

In the context of the present specification, the term “Harmonicfunction” relates to the field of mathematical physics and denotes afunction that satisfies Laplace's equation. Accordingly, applying theone or more Harmonic functions 1008 for restoring the smooth surface1010 within the gaps 1004 may be associated with setting certainboundary conditions.

Thus, according to some non-limiting embodiments of the presenttechnology, the boundary conditions for the one or more Harmonicfunctions 1008 may comprise vertex coordinates and respective vertexnormal vectors (not separately depicted in FIG. 11) defined atrespective vertices of those of the plurality of confirmed mesh elements1002, which are located at a boundary 1006 of the refined crown 3Drepresentation 1000. By doing so, the processor 550, using the one ormore Harmonic functions 1008, can be said to be configured to“propagate” smoothness of the refined crown 3D representation 1000 tothe augmented crown 3D representation 1020 of the crown portion 26, in asense, “patching” the gaps 1004 with the smooth surface 1010.

Additionally, according to certain non-limiting embodiments of thepresent technology, after restoring the smooth surface 1010 within therefined crown 3D representation 1000 of the crown portion 26, theprocessor 550 may be configured to redefine mesh elements associatedwith the augmented crown 3D representation 1020 generating a pluralityof augmented crown mesh elements 1022. According to some non-limitingembodiments of the present technology, the plurality of augmented crownmesh elements 1022 may be generated in such a way that vertices thereof(not separately depicted) are distributed therewithin substantiallyuniformly.

Thus, according to certain non-limiting embodiments of the presenttechnology, the augmented crown 3D representation 1020 of the crownportion 26, not including any digital garbage (that is, the imageartefacts 700) may further be used, by the processor 550, for a moreaccurate modelling of the movements of the tooth 15 when determining theorthodontic treatment.

The method 100 hence advances to step 106.

Step 106: Causing Display of the Augmented 3D Representation of theGiven Tooth Based on the Set of Confirmed Constrained Vertices.

With reference to FIG. 12, at step 106, having applied the method 100for identifying and eliminating the image artefacts 700 between alltooth 3D representations of the upper teeth 16 in the 3D model 600, theprocessor 550 may further be configured to generate an augmented 3Dmodel 1100 of the upper arch form 20, in accordance with certainnon-limiting embodiments of the present technology. As it can beappreciated, the augmented 3D model 1100 of the upper arch form 20 doesnot include the image artefacts 700 in the interdental spaces betweenrespective tooth 3D representations of the upper teeth 16 clearlydepicting a contour of each crown portion thereof (such as the crownportion 26 of the tooth 15).

Accordingly, in these embodiments, the processor 550 may be configuredto determine, based on the augmented 3D model 1100 of the upper archfrom 20, the orthodontic treatment for the subject by modellingrespective movements of each of the upper teeth 16 in an aggregatefashion, which may allow, for example, for more accurate and effectivedetection and avoidance of potential collisions between the associatedcrown portions of the upper teeth 16 in the course of the orthodontictreatment. Further, the processor 550 may be configured to output theaugmented 3D model 1100 in the screen 422 of the computer system 410 forprofessional control of the so determined orthodontic treatment by thepractitioner, as an example.

Needless to say that, in other non-limiting embodiments of the presenttechnology, the processor 550 may be configured to apply the same methodas described above, mutatis mutandis, within the 3D model 600, to toothrepresentations of the lower teeth 27, thereby generating an augmented3D model (not separately depicted) of the lower arch form 21 of thesubject for subsequent generation of an orthodontic treatment therefor.

In other non-limiting embodiments of the present technology, theaugmented crown 3D representation 1020 of the crown portion 26 sosegmented from the 3D model 600 may further be used, by the processor550, for reconstructing the root 3D representation 1620 of the rootportion 28 of the tooth 15. This may further allow, for example, fordetection and avoidance of potential collisions of the root portion 28with root portions of the adjacent teeth or damages to the upper gingiva36, for example, as will be described immediately below.

Thus, certain embodiments of the method 100 allow for more efficient andaccurate reconstruction of a 3D representation of the crown portion 26of the tooth 15 (such as the augmented crown 3D representation 1020)using raw image data indicative thereof provided by a conventionalintraoral scanner, without the need for acquiring and further mergingadditional image data generated by methods of CT- and/or MR-imaging.Accordingly, such an approach allows for a more accurate modelling ofthe tooth movements of the tooth 15 in the course of the plannedorthodontic treatment considering the movements the crown portion 26relative to crown portions of the respective ones of the upper teeth 16at an expected level of accuracy. In certain embodiments, this allowsdeveloping safer and more effective orthodontic treatments with limitedcomputational resources and inaccessibility of additional image data.

The method 100 hence terminates.

Root Portion Reconstruction

As alluded to above, according to certain non-limiting embodiments ofthe present technology, the processor 550 may be configured to use theaugmented crown 3D representation 1020 of the crown portion 26 generatedin accordance with the method 100 to generate the root 3D representation1620 of the root portion 28; further merge the augmented crown 3Drepresentation 1020 with the root 3D representation 1620, therebygenerating the tooth 3D representation 1720 of the tooth 15. The tooth3D representation 1720 of the tooth 15 may hence be used for a moreaccurate planning of the orthodontic treatment allowing taking intoaccount spatial positions of the root portion 28 within the uppergingiva 36, which may further enable avoiding possible collisionsthereof with root portions with other of the upper teeth 16 and damageto the upper gingiva 36, whether permanent or not.

To that end, according to some non-limiting embodiments of the presenttechnology, the processor 550 may be configured to execute a method 200for reconstructing a root 3D representation of a root portion associatedwith the tooth 15 (such as the root 3D representation 1620 of the rootportion 28), a flowchart diagram of which is depicted in FIG. 13.

Step 202: Acquiring a 3D Representation of the Crown Portion of theGiven Tooth

At step 202, according to some non-limiting embodiments of the presenttechnology, the processor 550 may be configured to acquire a 3D crownrepresentation associated with the tooth 15, such as the augmented crown3D representation 1020 of the crown portion 26.

Further, according to certain non-limiting embodiments of the presenttechnology, the processor 550 may be configured to acquire referencedata of the tooth 15. In these non-limiting embodiments, the referencedata of the tooth 15 may comprise, without limitation, at least one of anumber of root branches of the root portion 28; approximate overalldimensions of the tooth 15 including those of the crown portion 26 andof the root portion 28. To that end, the approximate overall dimensionsfor the tooth 15 may comprise respective dimensions of the tooth 15averaged over a sample of subjects, and variations thereof within thesample, as an example.

With reference to FIG. 14, there is depicted a schematic diagram of theaugmented crown 3D representation 1020 used by the processor 550 toreconstruct the root 3D representation 1620 of the root portion 28, inaccordance with certain non-limiting embodiments of the presenttechnology.

Certain non-limiting embodiments of the present technology are based ona premise that the augmented crown 3D representation 1020 may bepre-associated with a longitudinal tooth axis 1202 defining a directionfor generating the root 3D representation. In some non-limitingembodiments of the present technology, the longitudinal tooth axis 1202may be predetermined, by the processor 550, based on data indicative ofspecific anatomical features of crown portion 26 which includes, withoutbeing limited to: lobes, developmental grooves, and marginal ridges, asan example. In these embodiments, the data indicative of the specificanatomical features of the crown portion 26 may be part of the referencedata indicative of the tooth 15 and include data of spatial positionsand dimensions of at least some of the above-listed anatomical featuresof the crown portion 26 averaged over the sample of subjects.

In specific non-limiting embodiments of the present technology, thelongitudinal tooth axis 1202 may be a central tooth axis associated withthe tooth 15 having been determined, by the processor 550, based on theaugmented crown 3D representation 1020 as described in a co-owned U.S.patent application Ser. No. 16/877,972, entitled “SYSTEMS AND METHODSFOR DETERMINING TOOTH CENTER OF RESISTANCE”, and bearing an AttorneyDocket number 104117-093; the content of which is hereby incorporated byreference in its entirety.

The method 200 hence advances to step 204.

Step 204: Determining a Location of a Root Apex of the 3D Representationof the Root Portion Relative to the Predetermined Longitudinal ToothAxis, the Determining being Based on a Predetermined Instruction forLocating the Root Apex

With continued reference to FIG. 14, at step 204, according to certainnon-limiting embodiments of the present technology, based on thereference data of the tooth 15, the processor 550 may be configured todetermine, along the longitudinal tooth axis 1202, a location of a rootapex 1204 of the root 3D representation of the root portion 28.

The method advances to step 206.

Step 206: Generating, in a Reference Plane Dissecting the PredeterminedLongitudinal Tooth Axis and Based on the 3D Representation of the CrownPortion, a Closed Curve on the 3D Representation of the Crown Portion

According to some non-limiting embodiments of the present technology,the processor 550 may be configured to reconstruct the root 3Drepresentation 1620 based on curvature features of the augmented crown3D representation 1020 of the crown portion 26. To that end, to acquirecertain data of the curvature of the augmented crown 3D representation1020, at step 206, the processor 550 may be configured to construct aclosed curve around it.

With reference to FIG. 15, there is depicted a schematic diagram ofexecuting, by the processor 550, the step 206 of the method 200 toconstruct a closed curve 1304 around the augmented crown 3Drepresentation 1020 of the crown portion 26, in accordance with certainnon-limiting embodiments of the present technology.

According to some non-limiting embodiments of the present technology,the processor 550 may be configured to construct the closed curve 1304in a horizontal reference plane 1302 intersecting the longitudinal toothaxis 1202. How the horizontal reference plane 1302 may be defined is notparticularly limited and may, for example, be defined as beingperpendicular to the longitudinal tooth axis 1202. However, otherspatial positions of the horizontal reference plane 1302 may also beenvisioned by one of skill in the art. For example, the horizontalreference plane 1302 may be defined as extending through points of theaugmented crown 3D representation 1020 indicative of contact regions ofthe tooth 15 with other ones of the upper teeth 16 adjacent thereto, oras being parallel to such a plane.

As previously mentioned, in some non-limiting embodiments of the presenttechnology, the augmented crown 3D representation 1020 may berepresented by the plurality of augmented crown mesh elements 1022,wherein each mesh element is defined by respective vertices of aplurality of crown vertices 1322. Thus, in some non-limiting embodimentsof the present technology, the processor 550 may be configured toproject each one of the plurality of crown vertices 1322 onto thehorizontal reference plane 1302, thereby generating a set of projectedvertices 1306.

Further, in some non-limiting embodiments of the present technology, theprocessor 550 may be configured to determine the closed curve 1304 asextending through those of the set of projected vertices 1306 located atthe boundary thereof. In other words, the closed curve 1304 may comprisethose points from the set of projected vertices 1306 having most distantlocations from the longitudinal tooth axis 1304.

Additionally, in some non-limiting embodiments of the presenttechnology, the processor 550 may further be configured to smooth theclosed curve 1304. To that end, the processor 550 may be configured toexecute one or more smoothing algorithms, which may include, withoutbeing limited to: a kernel smoothing algorithm (such as an exponentialkernel algorithm, for example), a polynomial smoothing algorithm, aBezier smoothing algorithm, and the like.

Finally, the processor 550 may be configured to translate the horizontalreference plane 1302 containing the closed curve 1304 along thelongitudinal tooth axis 1202 to a predetermined height level 1402 of theaugmented crown 3D representation 1020, as depicted in FIG. 16, inaccordance with some non-limiting embodiments of the present technology.In some non-limiting embodiments of the present technology, thepredetermined height level may comprise a half of a height of theaugmented crown 3D representation 1020 of the crown portion 26. However,in other non-limiting embodiments of the present technology, thepredetermined height level 1402 may be determined based on coefficientsother than 0.5 applied to the height of the augmented crown 3Drepresentation 1020, such as 0.3, 0.4, 0.6, or 0.7, as being optimal fora particular implementation of the present technology.

How a height of the augmented crown 3D representation 1020 for executingsuch translation is determined is not limited, and may be determined,for example, in accordance with one of the techniques described in theco-owned U.S. patent application Ser. No. 16/877,972.

By doing so, the processor 550 may be configured to construct the closedcurve 1304 around the augmented crown 3D representation 1020, points ofwhich may be located either directly on a surface of the augmented crown3D representation 1020 or beyond it. Thus, the closed curve 1304 may besaid to be indicative of curvature of the augmented crown 3Drepresentation 1020 at its overall dimensions along the longitudinaltooth axis 1202. Further, as it can be appreciated, the closed curve1304 so positioned along the longitudinal tooth axis 1202 may be said todefine a boundary between the augmented crown 3D representation 1020 andthe root 3D representation 1620 within the tooth 3D representation 1720to be further constructed by the processor 550.

The method 200 hence advances to step 208.

Step 208: Segmenting the Closed Curve into a Plurality of Sub-Curves

At step 208, according to some none limiting embodiments of then presenttechnology, the processor 550 may be configured to segment the closedcurve 1304 into a plurality of sub-curves to form a respective segmentof the root 3D representation 1620.

With reference to FIGS. 17A and 17B, there is depicted a schematicdiagram of example execution, by the processor 550, of the step 208 forsegmenting the closed curve 1304 into a plurality of sub-curves 1502, inaccordance with certain non-limiting embodiments of the presenttechnology.

According to some non-limiting embodiments of the present technology,the processor 550 may be configured to generate the plurality ofsub-curves 1502 including a predetermined constant number thereof (suchas 32 or 64, for example), where each one of the plurality of sub-curves1502 has an equal length, as depicted in FIG. 17A. However, this mightnot be the case for implementing each and every non-limiting embodimentof the present technology, and non-equal length sub-curves are possible.

For example, in alternative non-limiting embodiments of the presenttechnology, each one of the plurality of sub-curves 1502 may begenerated by the processor 550, to form a same central angle relative tothe longitudinal tooth axis 1202 within the closed curve 1304. In otherwords, in these embodiments, the closed curve 1304 can be said to besegmented into the plurality of sub-curves 1502 by a plurality of lines1504 originating at a point of an intersection of the longitudinal toothaxis 1202 and the horizontal reference plane 1302 and extendingtherewithin, where angles between each two consecutive ones of theplurality of lines 1504 are equal, as depicted in FIG. 17B. Further, anumber of the plurality of lines 1504 may be selected to segment theclosed curve 1304 into the predetermined constant number of sub-curvesas mentioned above.

The method 200 hence proceeds to step 210.

Step 210: For Each One of the Plurality of Sub-Curves, Based on the RootApex and the Predetermined Longitudinal Tooth Axis, Generating aRespective Segment of a Plurality of Segments of the 3D Representationof the Root Portion, the Plurality of Segments of the 3D Representationof the Root Portion Comprising a Totality Thereof

At step 210, having generated the plurality of sub-curves 1502, theprocessor 550 may further proceed to generate the root 3D representation1620. With reference to FIG. 18, there is depicted a schematic diagramof executing, by the processor 550, the step 210 of the method 200 1600to generate a given segment 1612 of the root 3D representation 1620based on a given sub-curve 1602 of the plurality of sub-curves 1502, inaccordance with certain non-limiting embodiments of the presenttechnology.

First, according to some non-limiting embodiments of the presenttechnology, the processor 550 may be configured to identify a startpoint 1604 and an end point 1606 of the given sub-curve 1602. Further,the processor 550 may be configured to construct a Bezier curve 1608extending between the start point 1604 of the given sub-curve 1602 andthe root apex 1204.

How the Bezier curve 1608 is defined is not particularly limited; and insome non-limiting embodiments of the present technology, the Beziercurve 1608 may be initialized by a pair of tangent vectors originatingin its boundary points—that is, a first tangent vector 1614 originatingin the start point 1604 of the given sub-curve 1602, and a secondtangent vector 1616 originating in the root apex 1204. In theseembodiments, both the first tangent vector 1614 and the second tangentvector 1616 may be predefined to be mutually perpendicular, such thatthe first tangent vector 1614 may be parallel to the longitudinal toothaxis 1202, and the second tangent vector 1616 may be parallel to thehorizontal reference plane 1302 (and thus perpendicular to thelongitudinal tooth axis 1202). In turn, respective absolute values ofthe first tangent vector 1614 and the second tangent vector 1616 may bepredetermined based on respective orthogonal distances between the startpoint 1604 and the root apex 1204. Thus, for example, a first absolutevalue of the first tangent vector may be a half of a first orthogonaldistance 1618; and a second absolute value of the second tangent vector1616 may be a half of a second orthogonal distance 1628. It should benoted that, in other non-limiting embodiments of the present technology,other coefficients, such as 0.3 or 0.8, may be respectively applied tothe first orthogonal distance 1618 and the second orthogonal distance1628 to determine the absolute values of the first tangent vector 1614and the second tangent vector 1616.

Further, the processor 550 may be configured to revolve the Bezier curve1608 about the longitudinal tooth axis 1202 from the start point 1604 tothe end point 1606 of the given sub-curve 1602, thereby generating thegiven segment 1612 of the root 3D representation 1620. Thus, the givensegment 1612 can be said to be a segment of a revolution surface formedby revolving the Bezier curve 1608 about the longitudinal tooth axis1202.

The method 200 hence proceeds to step 212.

Step 212: Merging the 3D Representation of the Crown Portion with the 3DRepresentation of the Root Portion, Thereby Generating the 3DRepresentation of the Given Tooth

According to certain non-limiting embodiments of the present technology,a totality of segments so generated based on the respective ones of theplurality of sub-curves 1502 may thus form the root 3D representation1620 of the root portion 28, as depicted in FIG. 19.

Further, at step 212, the processor 550 may be configured to merge theroot 3D representation 1620 with the augmented crown 3D representation1020, thereby generating a tooth 3D representation 1720 of the tooth 15.

The method 200 further proceeds to step 214.

Step 214: Determining, Based on the 3D Representation of the GivenTooth, the Orthodontic Treatment for the Subject

At step 214, having applied the method 200, as described above withrespect to reconstructing the tooth 3D representation 1720 of the rootportion 28 of the tooth 15, to other ones of the upper teeth 16, theprocessor 550 may further be configured to generate respective root 3Drepresentations therefor, thereby completing the augmented 3D model 1100(depicted in FIG. 12) of the upper arch form 20. By so doing, in certainnon-limiting embodiments of the present technology, the processor 550may further be configured to generate the orthodontic treatment plan forthe subject causing the tooth 15 to move towards the aligned positionthat would account not only for movements of the crown portion 26, butwould also consider spatial positions of the root portion 28 within theupper arch form 20. This may allow for avoidance of collisions betweenthe root portion 28 and root portions of the upper teeth 16 adjacent tothe tooth 15 as well as prevent permanent damage to the upper gingiva 36and other tissues surrounding the tooth 15.

Additionally, the processor 550 may be configured to cause the computersystem 410 to display the so generated tooth 3D representations of theupper teeth 16 on the screen 422.

In some non-limiting embodiments of the present technology, beforecausing display of the tooth 3D representations of the upper teeth 16,the processor 550 may be configured to augment their associated rootportions for a more anatomically detailed representation of the upperarch form 20. More specifically, the processor 550 may be configured toreplace, within the tooth 3D representation 1720 of the tooth 15, theroot 3D representation 1620 of the root portion 28 with an augmentedroot 3D representation thereof, as will be immediately described below.

According to certain non-limiting embodiments of the present technology,the reference data associated with the tooth 15 may further include abase parametric 3D model of the root portion 28. With reference to FIG.20, there is depicted a base parametric 3D model 1802 for the rootportion 28 used, by the processor 550, for generating an augmented root3D representation 1804 thereof, in accordance with certain non-limitingembodiments of the present technology.

According to certain non-limiting embodiments of the present technology,the base parametric 3D model 1802 may comprise a plurality of coarseroot mesh elements 1822 that may further be smoothed, by the processor550, thereby generating the augmented root 3D representation 1804 of theroot portion 28.

In some non-limiting embodiments of the present technology, thesmoothing may be based on a subdivision surface algorithm 1806, to whichthe processor 550 may be provided access. Broadly speaking, thesubdivision surface algorithm 1806 may be configured to iterativelysubdivide each one of the plurality of coarse root mesh elements 1822into smaller ones of a plurality of augmented root mesh elements 1824,which is generated to correspond to the plurality of augmented crownmesh elements 1022.

In specific non-limiting embodiments of the present technology, thesubdivision surface algorithm 1806 may be a Catmull-Clark subdivisionsurface algorithm; however, in other non-limiting embodiments of thepresent technology, the subdivision surface algorithm 1806 may furtherinclude a Doo-Sabin subdivision surface algorithm, a Loop subdivisionsurface algorithm, a Midedge subdivision surface algorithm, and aKobbelt subdivision surface algorithm, as an example.

According to certain non-limiting embodiments of the present technology,the processor 550 may be configured to recursively apply the subdivisionsurface algorithm 1806 as long as a distribution of vertices along theplurality of augmented root mesh elements 1824 of the augmented root 3Drepresentation 1804 corresponds to that of vertices of the plurality ofaugmented crown mesh elements 1022 of the augmented crown 3Drepresentation 1020 depicted in FIG. 11.

It should further be noted that the processor 550 may be configured toverify, at each iteration of applying the subdivision surface algorithm1806, if dimensions of the augmented root 3D representation 1804correspond to the approximate overall dimensions of the root portion 28(such as a length thereof, for example) received as part of thereference data of the tooth 15, and adjust discrepancies therebetween.

Further, the processor 550 may be configured to merge the augmented root3D representation 1804 with the augmented crown 3D representation 1020generating an augmented tooth 3D representation 1902 depicted in FIG.21, in accordance with certain non-limiting embodiments of the presenttechnology.

In some non-limiting embodiments of the present technology, the mergingthe augmented root 3D representation 1804 and the augmented crown 3Drepresentation 1020 may produce an undefined region 1904 that mayfurther be smoothed, by the processor 550, using the one or moreHarmonic functions 1008 as described above with reference to FIG. 11.

Thus, the processor 550 may be configured to generate a respectiveaugmented tooth 3D representation for each of the upper teeth 16 andfurther cause display thereof on the screen 422 of the computer system410.

Additionally, in some non-limiting embodiments of the presenttechnology, to prevent intersections between the respective augmentedtooth 3D representations of the upper teeth 16 and hence generate morerealistic interdental spaces therebetween, the processor 550 may beconfigured to apply a collision detection and prevention methoddescribed in a co-owned U.S. patent application Ser. No. 16/703,424entitled “SYSTEMS AND METHODS FOR DETERMINING ORTHODONTIC TREATMENTS”,bearing an Attorney Docket No.: 104117-063, and filed on Dec. 4, 2019;the content of which is hereby incorporated by reference in itsentirety.

Thus, certain embodiments of the method 200 allow for more efficient andaccurate reconstruction of a 3D representation of the root portion 28 ofthe tooth 15 based on a respective 3D representation of the crownportion 26 (such as the augmented crown 3D representation 1020) usingimage data indicative thereof provided by a conventional intraoralscanner, without the need for acquiring and further merging additionalimage data generated by methods of CT- and/or MR-imaging. Accordingly,such an approach allows for a more comprehensive modelling of the toothmovements of the tooth 15 in the course of the planned orthodontictreatment considering the movements not only of the crown portion 26thereof, but also spatial positions of the root portion 28 relative, forexample, to other ones of the upper teeth 16 and those within the uppergingiva 36. In certain embodiments, this allows developing safer andmore effective orthodontic treatments with limited computationalresources and inaccessibility of additional image data.

The method 200 hence terminates.

Finally, to complete the generation of the comprehensive 3Drepresentation of the upper arch form 20 (such as a comprehensive 3Drepresentation 3200 depicted in FIG. 35), after the generating theaugmented tooth 3D representation 1902, the processor 550 may further beconfigured to generate a comprehensive gingiva 3D representation of theupper gingiva 36, as will be described immediately below.

Gingiva Reconstruction

As previously mentioned, for determining a more effective and efficientorthodontic treatment plan, it may be necessary to consider toothmovements of the tooth 15 within the subject's arch form (such as theupper arch form 20) in its entirety. For example, this may be the casewhen considering movements of the root portion 28 within the uppergingiva 36 during the orthodontic treatment to prevent permanent damagethereof or to tissues related thereto (such as proximal nerve pathwaysand blood vessels). In another example, more accurate image data of anactual anatomy of the upper gingiva 36 (such as overall dimensionsthereof) may allow for a more efficient process for producing theorthodontic appliance 10 (described above with reference to FIGS. 1 and2), quality of which may be directly connected with the overall qualityof the planned orthodontic treatment.

However, intra-oral scanning techniques (such as those describedhereinabove in respect of the imaging device 430 of FIG. 4) may not beeffective in capturing the comprehensive gingiva 3D representation (suchas a comprehensive gingiva 3D representation 3100 depicted in FIGS. 34and 35) of the upper gingiva 36 as they may be limited only to visuallyaccessible portions thereof, which may not be sufficient for consideringthe aspects of the orthodontic treatment mentioned above.

Thus, according to certain non-limiting embodiments of the presenttechnology, the processor 550 may be configured to execute a method 300for reconstructing a gingiva 3D representation of the upper gingiva 36for the upper arch form 20, a flowchart diagram of which is depicted inFIG. 22.

Step 302: Acquiring a 3D Representation of an Arch Form Associated withthe Subject, the 3D Representation Including A Representation of theGingiva and a Plurality of Teeth of the Subject

The method 300 commences at step 302 with the processor 550 acquiring araw 3D representation of the upper arch form 20 of the subject. Withreference to FIG. 23, there is depicted a portion of the 3D model 600 ofFIG. 6 representative of frontal view of a raw arch form 3Drepresentation 2000 of the upper arch form 20 including a raw gingiva 3Drepresentation 2006 of the upper gingiva 36 received, by the processor550, from the imaging device 430, in accordance with certainnon-limiting embodiments of the present technology.

As it can be appreciated, the raw gingiva 3D representation 2006 has anuneven contour, which may be indicative that a significant portion ofthe upper gingiva 36 was not accessible to the imaging device 430 forcapturing at the moment of generating the raw gingiva 3D representation2006.

Further, in some non-limiting embodiments of the present technology, theimaging device 430 may be configured to generate the raw gingiva 3Drepresentation 2006 comprising a plurality of raw mesh elements 2004. Tothat end, the plurality of raw mesh elements 2004 may be chaoticallydistributed on a surface of the raw gingiva 3D representation 2006,whose coordinates should be determined by the processor 550 for furtherprocessing. However, the process for determining these coordinates maybe computationally costly, and as a result, this may pose additionalchallenges to apply textures and colours onto the raw gingiva 3Drepresentation 2006 depicting anatomical features of the upper gingiva36 for effective visualization thereof on the screen 422 of the computersystem 410. Accordingly, this may compromise accuracy of the orthodontictreatment of the upper arch form 20 of the subject.

Thus, certain non-limiting embodiments of the present technology aredirected to methods and systems for reconstructing the comprehensivegingiva 3D representation of the upper gingiva 36 used for determining asafer and more effective orthodontic treatment, which will be describedimmediately below.

With reference to FIG. 24, there is depicted a perspective view of theraw arch form 3D representation 2000 of the upper arch form 20, inaccordance with certain non-limiting embodiments of the presenttechnology.

According to certain non-limiting embodiments of the present technology,the processor 550 may first be configured to determine a jaw coordinatesystem 2105 associated with the raw arch form 3D representation 2000. Tothat end, along the image data indicative of the upper arch form 20, theprocessor 550 may be configured to receive data indicative of atransverse plane 2102 associated with a subject's skull. In the contextof the present disclosure, the term “transverse” plane relates to thefield of anatomy of vertebrates (including humans) and denotes animaginary plane dividing a body into superior and inferior parts. Thetransverse plane 2102, as referred to herein, is perpendicular to acoronal plane and a sagittal plane associated with the subject's skull.In other non-limiting embodiments of the present technology, thetransverse plane 2102 may be a Frankfort horizontal plane associatedwith the subject's skull.

Further, the processor 550 may be configured to receive data of a commonmedian axis 2104. In the context of the present disclosure, the term“common median axis” is to denote a line extending within the transverseplane 2102 and parallel to an imaginary line extending between eithercentral ones of the upper teeth 16 or central ones of the lower teeth 27(not separately numbered) of the subject, which may also be referred toherein a midline of the upper arch form 20 or a midline of the lowerarch form 21, respectively. Thus, for example, those of the upper teeth16 located towards the common median axis 2104 may be referred to asmesial teeth; and those of the upper teeth 16 located away from thecommon median axis may be referred to as distal teeth.

Finally, the processor 550 may be configured to generate a commonvertical axis 2106 to be parallel to the common median axis 2104. Thus,the processor 550 may be configured to determine the jaw coordinatesystem 2105, where an XY plane is parallel to the transverse plane 2102,a Y axis is parallel to the common median axis 2104, and a Z axis isparallel to the common vertical axis 2106.

The method 300 thus proceeds to step 304.

Step 304: Segmenting, in the 3D Representation of the Arch Form,Associated Representations of the Plurality of Teeth and the Gingiva toGenerate a Plurality of Segmentation Loops, Each Segmentation Loop beingRespectively Associated with Each Tooth of the Plurality of Teeth andRepresenting an Interface of a Given Tooth with the Gingiva

At step 304, according to certain non-limiting embodiments of thepresent technology, the processor 550 may be configured to isolate theraw gingiva 3D representation 2006 from the raw arch form 3Drepresentation 2000. To that end, the processor 550 may be configured todetermine contours of the respective tooth 3D representations of theupper teeth 16 in the raw arch form 3D representation 2000 and removethem therefrom. Thus, in some non-limiting embodiments of the presenttechnology, the processor 550 may be configured to apply a toothsegmentation technique described in the section Automatic ToothSegmentation of the present document. In other non-limiting embodimentsof the present technology, the processor 550 may be configured to applyanother automatic tooth segmentation technique, for example, one, whichis described in a co-owned U.S. patent application Ser. No. 16/703,471filed Dec. 4, 2019, entitled “METHOD AND SYSTEM FOR DENTAL BOUNDARYDETERMINATION”, and bearing an Attorney Docket number 104117-074; thecontent of which is hereby incorporated by reference in its entirety.

With reference to FIG. 25, there is depicted the raw gingiva 3Drepresentation 2006 including a plurality of preliminary segmentationloops 2202 representing interface for upper teeth 16 and generated, bythe processor 550, by segmenting the tooth 3D representations of the inthe raw arch form 3D representation 2000, in accordance with certainnon-limiting embodiments of the present technology.

In some non-limiting embodiments of the present technology, theprocessor 550 may be configured to filter out those vertices associatedwith respective ones of the plurality of raw mesh elements 2004 that arelocated on representations on interdental papillae, between each pair ofadjacent ones of the plurality of preliminary segmentation loops 2202.In other words, the processor 550 may be configured to filter out thosevertices associated with respective ones of the plurality of raw meshelements 2004 that are shared between the adjacent ones of the pluralityof preliminary segmentation loops 2202.

For example, a first preliminary segmentation loop 2204 is adjacent to asecond preliminary segmentation loop 2205, such that both of them arecoupled by a representation of a given interdental papilla 2206. To thatend, the representation of the given interdental papilla 2206 mayinclude mesh elements of the plurality of raw mesh elements 2004 sharedbetween the first preliminary segmentation loop 2204 and the secondpreliminary segmentation loop 2205, which the processor 550 may thus beconfigured to remove.

In some non-limiting embodiments of the present technology, theprocessor 550 may be configured to remove all mesh elements of theplurality of raw mesh elements 2004 lying within a circle 2208 of apredetermined radius (not separately numbered) defined at a tip of therepresentation of the given interdental papilla 2206. A length of thepredetermined radius may depend, for example, on a particularconfiguration of the imaging device 430, and, in certain non-limitingembodiments of the present technology, may be 1 mm. However, in othernon-limiting embodiments of the present technology, the length of thepredetermined radius of the circle 2208 may take other values, such as0.5 mm, 1.5 mm, or 3 mm, as an example.

Thus, the processor 550 may be configured to remove mesh elements of theplurality of raw mesh elements 2004 lying on the respectiverepresentations of interdental papillae between each pair of adjacentones of the plurality of preliminary segmentation loops 2202.

Further, the processor 550 may be configured to close each one of theplurality of preliminary segmentation loops 2202, thereby generating aplurality of closed preliminary segmentation loops 2302, as depicted inFIG. 26, in accordance with certain non-limiting embodiments of thepresent technology. To close each one of the plurality of preliminarysegmentation loops 2202, the processor 550 may be configured to use, forexample, linear segments extending between respective ends thereof.However, segments of various curvatures may be used for closing each oneof the plurality of preliminary segmentation loops 2202 depending on aparticular implementation of the present technology.

Additionally, in some non-limiting embodiments of the presenttechnology, the processor 550 may be further configured to smooth eachof the plurality of closed preliminary segmentation loops 2302 using oneof the techniques described above in respect of smoothing the closedcurve 1304.

Also, in some non-limiting embodiments of the present technology, theprocessor 550 may be configured to redefine certain mesh elements of theplurality of raw mesh elements 2004 respectively representative of eachof the plurality of closed preliminary segmentation loops 2302 such thata plurality of loop vertices 2306 associated with a given closedpreliminary segmentation loop 2304 are equally spaced. In somenon-limiting embodiments of the present technology, the processor 550may be further configured to maintain a predetermined number of verticesin the plurality of loop vertices 2306 (such as 90 vertices, forexample), based, for example, on a trade-off between a quality of thecomprehensive gingiva 3D representation 3100 and computationalcomplexity and/or demand associated with the generation thereof.

Further, with reference to FIG. 27, according to some non-limitingembodiments of the present technology, the processor 550 may beconfigured to translate each one of the plurality of closed preliminarysegmentation loops 2302 along a respective longitudinal tooth axis (suchas the longitudinal tooth axis 1202 associated with the tooth 15described above with reference to FIG. 14) at a predeterminedtranslation distance 2402. By so doing, the processor 550 may beconfigured to compensate for a possible chamfer effect produced by theimaging device 430 when generating the raw arch form 3D representation2000. Thus, a given value of the predetermined translation distance 2402may depend, inter alia, on a specific configuration of the imagingdevice 430, and in specific non-limiting embodiments of the presenttechnology, may be, for example, 0.25 mm.

Finally, with reference to FIG. 28, according to some non-limitingembodiments of the present technology, the processor 550 may beconfigured to project each one of the plurality of closed preliminarysegmentation loops 2302 onto a respective one of tooth 3Drepresentations (such as the tooth 3D representation 1720 of the tooth15 described above with reference to FIG. 19) of the upper teeth 16,thereby generating a plurality of segmentation loops 2502, which mayfurther be used for generating the comprehensive gingiva 3Drepresentation 3100 of the upper gingiva 36.

For example, the processor 550 may be configured to project the givenclosed preliminary segmentation loop 2304 onto the tooth 3Drepresentation 1720 projecting each vertex (not separately numbered)representative thereof onto the tooth 3D representation 1720 along arespective shortest path thereto, thereby generating a givensegmentation loop 2504 of the plurality of segmentation loops 2502.

According to certain non-limiting embodiments of the present technology,the processor 550 may further be configured to generate a central curvethrough the plurality of segmentation loops 2502.

The method 300 hence advances to step 306.

Step 306: Determining, Between Each Adjacent Two Segmentation Loops ofthe Plurality of Segmentation Loops, a Midpoint, Thereby Generating aPlurality of Primary Midpoints for the Plurality of Segmentation Loops;

With reference to FIG. 29, at step 306, by the processor 550 may beconfigured to identify points to generate a primary central curve 2602,in accordance with certain non-limiting embodiments of the presenttechnology.

According to certain non-limiting embodiments of the present technology,the processor 550 may first be configured to identify, for each one ofthe plurality of segmentation loops 2502, a point thereof that isclosest to an adjacent segmentation loop. For example, on the givensegmentation loop 2504, the processor 550 may be configured to identifya first closest point 2604 that is closest to an adjacent segmentationloop 2506. By the same token, the processor 550 may be configured toidentify, on the adjacent segmentation loop 2506, a second closest point2606, which is closest to the given segmentation loop 2504 (in otherwords, to the first closest point 2604).

Further, based on the first closest point 2604 and the second closestpoint 2606, the processor 550 may be configured to determine a givenprimary midpoint 2608 of a plurality of primary midpoints 2610. In somenon-limiting embodiments of the present technology, the processor 550may be configured to determine the given primary midpoint 2608, forexample, as a midpoint between the first closest point 2604 and thesecond closest point 2606 within the jaw coordinate system 2105.

The method 300 hence proceeds to step 308.

Step 308: Based on the Plurality of Midpoints, Generating a PrimaryCentral Curve Along a First Horizontal Plane Parallel to the TransversePlane;

At step 308, based on the plurality of primary midpoints 2610, theprocessor 550 may be configured to generate the primary central curve2602. For example, the processor 550 may be configured to generate theprimary central curve 2602 by joining each one of the plurality ofprimary midpoints 2610 by a respective curve segment (not separatelydepicted). In some non-limiting embodiments of the present technology,the respective curve segment may be a segment of a second order Beziercurve. However, it should be noted that how curvature of the respectivecurve segment may be defined is not limited, and in other non-limitingembodiments of the present technology, it may also be defined, forexample, by a cubic Bezier curve.

Also, in those non-limiting embodiments of the present technology (notdepicted) where certain of the upper teeth 16 are missing (previouslyextracted or destroyed, for example) forming respective blank spaces inthe plurality of segmentation loops 2502, the processor 550 may furtherbe configured to extrapolate the primary central curve 2602 within therespective blank spaces based on curvature thereof associated with thoseof the upper teeth 16 adjacent to the blank spaces. The same applies tothose of the plurality of segmentation loops 2502 having no secondadjacent segmentation loop, such as those representative of most distalones of the upper teeth 16 within the upper arch form 20.

Further, according to certain non-limiting embodiments of the presenttechnology, the processor 550 may be configured to join each pair ofadjacent ones of the plurality of segmentation loops 2502 by respectivearcs representative of interdental papillae of the comprehensive gingiva3D representation.

With reference to FIG. 30, there is depicted a schematic diagram of aprimary border curve 2702 generated by the processor 550 based onjoining adjacent ones of the plurality of segmentation loops 2502, inaccordance with certain non-limiting embodiments of the presenttechnology.

As it can be appreciated, the primary central curve 2602 divides eachone of the given segmentation loop 2504 and the adjacent segmentationloop 2506 into a first outer portion 2704, a first inner portion 2705, asecond outer portion 2706, and a second inner portion 2707,respectively. Further, according to some non-limiting embodiments of thepresent technology, the processor 550 may be configured to determine arespective length of each one of the first outer portion 2704, the firstinner portion 2705, the second outer portion 2706, and the second innerportion 2707. Finally, based on the respective length, the processor 550may further be configured to identify an outer pair of points 2708 andan inner pair of points 2709 to generate an outer arc 2710 and an innerarc 2711, thereby interconnecting the given segmentation loop 2504 withthe adjacent segmentation loop 2506.

In some non-limiting embodiments of the present technology, theprocessor 550 may be configured to identify the outer pair of points2708 and the inner pair of points 2709 based on predeterminedcoefficients applied to the respective length of each of the first outerportion 2704, the first inner portion 2705, the second outer portion2706, and the second inner portion 2707. As such, each one of the outerpair of points 2708 and the inner pair of points 2709 may be located ata predetermined level of the respective length of one of the first outerportion 2704, the first inner portion 2705, the second outer portion2706, and the second inner portion 2707.

For example, the processor 550 may be configured to identify a first oneof the outer pair of points 2708, lying on the first outer portion 2704,and a first one of the inner pair of points 2709, lying on the firstinner portion 2705, to be located at a 0.75 level of the respectivelength associated therewith. By the same token, the processor 550 may beconfigured to identify a second one of the outer pair of points 2708,lying on the second outer portion 2706, and a second one of the innerpair of points 2709, lying on the second inner portion 2707, to belocated on a 0.25 level of the respective length associated therewith.It should be expressly understood that other predetermined coefficientsmay also be applied, in alternative non-limiting embodiments of thepresent technology, depending, inter alia, on a specific anatomicalconfiguration (such as a type thereof) of an associated one of the upperteeth 16.

Having identified each one of the outer pair of points 2708 and theinner pair of points 2709, the processor 550 may further be configuredto generate the outer arc 2710 and the inner arc 2711 based on curvatureof the given segmentation loop 2504 and the adjacent segmentation loop2506. For example, the processor 550 may be configured to generate oneof the outer arc 2710 and the inner arc 2711 maintaining (in a sense,propagating) curvature of one of the given segmentation loop 2504 andthe adjacent segmentation loop 2506. By doing so, the processor 550 maybe configured to interconnect each pair of adjacent ones of theplurality of segmentation loops 2502 generating the primary border curve2702.

According to certain non-limiting embodiments of the present technology,after generating the primary border curve 2702, the processor 550 mayfurther be configured to generate, between each pair of adjacent ones ofthe plurality of segmentation loops 2502, a respective tween curve thatmay be used for joining gingiva segments (generation of which will bedescribed below) of the comprehensive gingiva 3D representation 3100with the primary border curve 2702.

With reference to FIG. 31, there is depicted a schematic diagram of astep of a process for generating, by the processor 550, a given tweencurve 2804 of a plurality of tween curves 2802, in accordance withcertain non-limiting embodiments of the present technology.

According to certain non-limiting embodiments of the present technology,the processor 550 may be configured to generate the given tween curve2804 to originate in the given primary midpoint 2608, based on the givensegmentation loop 2504 and the adjacent segmentation loop 2506. Forexample, the processor 550 may be configured to generate the given tweencurve 2804 based on a first loop segment 2806 and a second loop segment2808 respectively defined on the given segmentation loop 2504 and theadjacent segmentation loop 2506 between respective ones of the outerpair of points 2708 and the inner pair of points 2709 lying thereon.

In some non-limiting embodiments of the present technology, theprocessor 550 may be configured to generate the given tween curve 2804as an average curve of the first loop segment 2806 and the second loopsegment 2808. To that end, according to these embodiments, the processor550 may be configured to use one or more curve fitting techniques, whichmay include, without being limited to, one or more of: a linear curvefitting technique, a non-linear curve fitting technique, including, forexample, a polynomial curve fitting technique, an exponential curvefitting technique, a logarithmic curve fitting technique, a spline curvefitting technique, and the like.

Additionally, in some non-limiting embodiments of the presenttechnology, the processor 550 may be configured to adjust respectivespatial positions of the outer arc 2710 and that of the inner arc 2711such that they intersect with the given tween curve 2804, for example,in an outer intersection point 2810 and in an inner intersection point2812. By doing so, the processor 550 may be configured to generate,based on the primary border curve 2702, a border curve 2820.

Having generated the plurality of tween curves 2802, the processor 550may thus be configured to use it as a frame for generation of thegingiva segments based on the border curve 2820, thereby generating thecomprehensive gingiva 3D representation 3100, as will be describedimmediately below.

According to certain non-limiting embodiments of the present technology,the generating a given gingiva segment may further comprise generating,the processor 550, a respective inner and outer mesh curves, and joiningthem with the border curve 2820 using the plurality of tween curves2802.

The method 300 hence advances to step 310.

Step 310: Generating, Based on the Primary Central Curve, A First InnerMesh Curve and a First Outer Mesh Curve, the First Inner Mesh CurvePositioned Along a Second Horizontal Plane and the First Outer MeshCurve Positioned Along a Third Horizontal Plane, Both the SecondHorizontal Plane and the Third Horizontal Plane being Parallel to theTransverse Plane and being Vertically Offset, Along the Common VerticalAxis, from the First Horizontal Plane

With reference to FIGS. 32A and 32B, there is depicted a schematicdiagram of executing, by the processor 550, step 310 of the method 300to generate a first gingiva segment 2900, in accordance with certainnon-limiting embodiments of the present technology.

First, the processor 550 may be configured to generate a first outermesh curve 2902 and a first inner mesh curve 2904. In some non-limitingembodiments of the present technology, the processor 550 may beconfigured to generate the first outer mesh curve 2902 and the firstinner mesh curve 2904 by projecting the primary central curve 2602 ontoa first horizontal plane (not depicted) and a second horizontal plane(not depicted), respectively.

In some non-limiting embodiments of the present technology, theprocessor 550 may be configured to determine the first horizontal plane(not depicted) and the second horizontal plane (not depicted) to beparallel to the XY plane associated with the jaw coordinate system 2105and vertically offset, along the Z axis, from the border curve 2820. Forexample, the processor 550 may be configured to determine: (1) the firsthorizontal plane (not depicted) to be vertically offset from a highestvertex of the border curve 2820 along the Z axis associated with the jawcoordinate system 2105 at a first predetermined vertical distance; and(2) the second horizontal plane (not depicted) to be vertically offsetfrom the highest vertex of the border curve 2820 along the Z axis at asecond predetermine vertical distance. Generally speaking, the firstpredetermined vertical distance and the second predetermined verticaldistance have different values, which, in some non-limiting embodimentsof the present technology may be, for example, 5 mm and 6 mm,respectively. In other non-limiting embodiments of the presenttechnology, the first predetermined vertical distance and the secondpredetermined vertical distance may be equal, that is, the firsthorizontal plane (not depicted) and the second horizontal plane (notdepicted) may comprise a same horizontal plane.

Further, having generated the first outer mesh curve 2902 and the firstinner mesh curve 2904 in the first horizontal plane (not depicted) andthe second horizontal plane (not depicted), respectively, the processor550 may be configured to offset them horizontally therewithin relativeto a horizontal projection of the primary central curve 2602 onto the XYplane associated with the jaw coordinate system 2105, that is, along theY axis associated with the jaw coordinate system 2105. For example, theprocessor 550 may be configured to offset the first outer mesh curve2902 along the Y axis anteriorly relative to the primary central curve2602 at an anterior horizontal distance 2906. Further, the processor 550may be configured to offset the first inner mesh curve 2904 along the Yaxis posteriorly relative to the primary central curve 2602 at aposterior horizontal distance 2908. Broadly speaking, the anteriorhorizontal distance 2906 and the posterior horizontal distance 2908 mayhave different values, and in some non-limiting embodiments of thepresent technology, may vary within a distance value range from 10 mm to12 mm, as an example. However, in other non-limiting embodiments of thepresent technology, the anterior horizontal distance 2906 and theposterior horizontal distance 2908 may be equal.

Additionally, the processor 550 may be configured to modulate each oneof the first outer mesh curve 2902 and the first inner mesh curve 2904adjusting respective curvature thereof accounting for specificanatomical features of the upper gingiva 36 of the subject.

According to certain non-limiting embodiments of the present technology,the processor 550 may further be configured to modulate a respectivelength of each one of the primary central curve 2602, the first outermesh curve 2902, and the first inner mesh curve 2904. For example, theprocessor 550 may be configured to cut each one of the primary centralcurve 2602, the first outer mesh curve 2902, and the first inner meshcurve 2904 by a perpendicular plane (not separately depicted) parallelto an XZ plane associated with the jaw coordinate system 2105 andlocated at a predetermined horizontal distance anteriorly, along the Yaxis, from a most posterior vertex of the raw gingiva 3D representation2006 (depicted in FIG. 24). In some non-limiting embodiments of thepresent technology, this predetermined distance may be, however, notlimited to, 2 mm.

The method further proceeds to step 312.

Step 312: Projecting the Plurality of Primary Midpoints onto the FirstInner Mesh Curve and the First Outer Mesh Curve, Thereby Generating aFirst Plurality of Inner Midpoints and a First Plurality of OuterMidpoints

At step 312, according to certain non-limiting embodiments of thepresent technology, based on the plurality of primary midpoints 2610,the processor 550 may be configured to generate a first plurality ofouter midpoints 2910 and a first plurality of inner midpoints 2912respectively associated with the first outer mesh curve 2902 and thefirst inner mesh curve 2904. To that end, in some non-limitingembodiments of the present technology, the processor 550 may beconfigured to project the plurality of primary midpoints 2610 onto eachone of the first outer mesh curve 2902 and the first inner mesh curve2904 maintaining same distribution of midpoints of the first pluralityof outer midpoints 2910 and the first plurality of inner midpoints 2912therewithin as that of the plurality of primary midpoints 2610 withinthe primary central curve 2602. For example, the processor 550 may beconfigured to calculate relative distances between each neighboring onesof the plurality of primary midpoints 2610, and based on a length of theprimary central curve 2602, determine a respective weight coefficientfor distributing midpoints of the first plurality of outer midpoints2910 and the first plurality of inner midpoints 2912 within the firstouter mesh curve 2902 and the first inner mesh curve 2904, respectively.

The method further proceeds to step 314.

Step 314: Generating a First Segment of the Reconstructed 3DRepresentation of the Gingiva by Joining Each One from the Plurality ofPrimary Midpoints with Respective Ones from the First Plurality of InnerMidpoints and from the First Plurality of Outer Midpoints

At step 314, having generated the first plurality of outer midpoints2910 and the first plurality of inner midpoints 2912, the processor 550can be said to have generated a plurality of midpoint triplets 2920including a respective one from the first plurality of outer midpoints2910, a respective one from the plurality of primary midpoints 2610, anda respective one from the plurality of inner midpoints 2912.Accordingly, by interconnecting each one of the plurality of midpointtriplets 2920 using a respective one of the plurality of tween curves2802, the processor 550 may be configured to generate the first gingivasegment 2900 of the comprehensive gingiva 3D representation of the uppergingiva 36.

With reference to FIG. 33, following the same approach described abovein respect of generating the first gingiva segment 2900, the processor550 may be configured to generate a second gingiva segment 3000 of thecomprehensive gingiva 3D representation 3100, in accordance with certainnon-limiting embodiments of the present technology. To that end, theprocessor 550 may be configured to generate a second outer mesh curve3002 and a second inner mesh curve 3004 by projecting the primarycentral curve 2602 onto a third horizontal plane (not depicted) and afourth horizontal plane (not depicted), respectively. The processor 550may be configured to construct the third horizontal plane (not depicted)and the fourth horizontal plane (not depicted) to be parallel to andvertically offset from a respective one of the first horizontal plane(not depicted) and the second horizontal plane (not depicted) at a thirdpredetermined vertical distance that, according to specific non-limitingembodiments of the present technology, may be 0.4 mm, as an example.

Further, the processor 550 may be configured to generate, based on theplurality of primary midpoints 2610, a second plurality of outermidpoints 3010 and a second plurality of inner midpoints 3012respectively associated with the second outer mesh curve 3002 and thesecond inner mesh curve 3004 in a similar fashion described above inrespect of the first plurality of outer midpoints 2910 and the firstplurality of inner midpoints 2912, respectively.

Finally, extending each one of the plurality of tween curves 2802through a respective one from the first plurality of outer midpoints2910 and a respective one from the second plurality of outer midpoints3010; and further through a respective one from the first plurality ofinner midpoints 2912 and a respective one from the second plurality ofinner midpoints 3012, the processor 550 may thus be configured togenerate the second gingiva segment 3000.

In additional non-limiting embodiments of the present technology, theprocessor 550 may further be configured to generate a second pluralityof tween curves 3006. To that end, to generate a given one of the secondplurality of tween curves 3006, the processor 550 may be configured togenerate, on the given segmentation loop 2504 of the plurality ofsegmentation loops 2502, an additional pair of points (not depicted).For example, the processor 550 may be configured to generate each one ofthe additional pair of points (not depicted) to correspond to a 0.5level of the respective length of the first outer portion 2704 and thefirst inner portion 2705 (see FIG. 30) of the given segmentation loop2504. Further, the processor 550 may be configured to generate the givenone of the second plurality of tween curves 3006 extending though theadditional pair of points (not depicted) on the given segmentation loop2504 similar to the generating the given tween curve 2804 of theplurality of tween curves 2802.

Finally, the processor 550 may be configured to extend each one of thesecond plurality of tween curves 3006 through (1) the first outer meshcurve 2902 and the second outer mesh curve 3002; and (2) the first innermesh curve 2904 and the second inner mesh curve 3004. This is believedto allow achieving a desired level of granularity of the comprehensivegingiva 3D representation 3100 of the upper gingiva 36.

It should be expressly understood that following the above approach togenerating the second plurality of tween curves 3006, to achieve adesired level of granularity of the comprehensive gingiva 3Drepresentation 3100, the processor 550 may be configured to generateadditional pluralities of tween curves at respective levels of theassociated lengths of the first outer portion 2704 and the first innerportion 2705 of the given segmentation loop 2504.

Accordingly, based on predetermined dimensions for the comprehensivegingiva 3D representation 3100 (that in turn may be indicative of anaverage gingiva height, for example), the processor 550 may beconfigured to generate additional, such as 3 or 4, gingiva segmentsfollowing the approach described above in respect of generating thefirst gingiva segment 2900 and the second gingiva segment 3000. By sodoing the processor 550 can be said to use a “scaffolding” technique ofgenerating a respective gingiva segment, thereby generating a basegingiva cage 3102 of the comprehensive gingiva 3D representation 3100 asdepicted in FIG. 34, in accordance with certain non-limiting embodimentsof the present technology.

As it can be appreciated, the base gingiva cage 3102 is represented by aplurality of ordered quadrilateral mesh elements 3104 allowing theprocessor 550 to apply textures and colours thereto easier than to theplurality of raw mesh elements 2004 initially provided by the imagingdevice 430, which, in turn, may significantly save the computationalresources of the computer system 410.

Also, in some non-limiting embodiments of the present technology, beforethe applying the textures and colours to the base gingiva cage 3102,thereby generating the comprehensive gingiva 3D representation 3100, theprocessor 550 may be configured to apply the Catmull-Clark subdivisionsurface algorithm to the plurality of ordered quadrilateral meshelements 3104 to achieve the desired level of granularity and smoothness(such as that corresponding to one of the plurality of augmented crownmesh elements 1022 and plurality of augmented root mesh elements 1824)of a surface of the comprehensive gingiva 3D representation 3100.

The method 300 finally advances to step 316.

Step 316: Causing Display of the First Segment of the Reconstructed 3DRepresentation of the Gingiva.

With reference to FIG. 35, according to certain non-limiting embodimentsof the present technology, after texturizing the base gingiva cage 3102,thereby generating the comprehensive gingiva 3D representation 3100, atstep 316, the processor 550 may further be configured to merge it withthe tooth 3D representations (such as the tooth 3D representation 1720or the augmented tooth 3D representation 1902 of the tooth 15 depictedin FIGS. 19 and 21, respectively, as an example) of the upper teeth 16.By doing so, the processor 550 may be configured to generate thecomprehensive 3D representation 3200 of the upper arch form 20.

In additional non-limiting embodiments of the present technology, theprocessor 550 may further be configured to output the comprehensive 3Drepresentation 3200 of the upper arch form 20 on the screen 422 of thecomputer system 410. Accordingly, a practitioner having access to thecomputer system 410 may thus be able to use the comprehensive 3Drepresentation 3200 for modelling the tooth movements of the tooth 15within the upper arch form 20 considering mutual spatial positionsthereof with at least one of the adjacent teeth and effects of themodelled tooth movements, inter alia, onto the upper gingiva 36 ensuringthe safer and more efficient orthodontic treatment plan.

Thus, certain embodiments of the method 300 allow for more efficient andaccurate reconstruction of a 3D representation of the upper gingiva 36(such as the comprehensive gingiva 3D representation 3100) based on rawimage data indicative thereof and raw image data of the crown portions(such as the raw crown 3D representation 800 of the crown portion 26 ofthe tooth 15) of the upper teeth 16 provided by a conventional intraoralscanner, without the need for acquiring and further merging additionalimage data generated by methods of CT- and/or MR-imaging. Accordingly,such an approach allows for a more comprehensive modelling of the toothmovements of the tooth 15 in the course of the planned orthodontictreatment considering spatial positions of the root portion 28 thereofwithin the upper gingiva 36. In certain embodiments, this allowsdeveloping safer and more effective orthodontic treatments with limitedcomputational resources and inaccessibility of additional image data.

Further, certain embodiments of the method 300 allow for morecomputationally efficient application of textures and colours to thecomprehensive gingiva 3D representation 3100 for more effectivevisualization thereof on the screen 422 of the computer system 410increasing accuracy of the planned orthodontic treatment.

Finally, certain embodiments of the method 300 allow for a moreefficient production (for example, by means of 3D printing) of aligners(such as those made from composite materials), based on thecomprehensive gingiva 3D representation 3100, for conducting the sodetermined orthodontic treatment, as expected overall dimensions thereofmay allow more efficient planning of material consumption.

The method 300 hence terminates.

Needless to say that, in additional non-limiting embodiments of thepresent technology, the processor 550 may be configured to apply,mutatis mutandis, the methods 100, 200, and 300 for crown, root, andgingiva reconstruction, respectively, to generate a comprehensive 3Drepresentation of the lower arch form 21 including that of the lowerteeth 27 and the lower gingiva 37, as well as determine anotherorthodontic treatment based thereon, which is believed to be apparent toone skilled in the art.

It should further be noted that, in some non-limiting embodiments of thepresent technology, each of the method 100, the method 200, and themethod 300 may be executed, by the processor 550, separately and/orindependently based on respective input data. However, in othernon-limiting embodiments of the present technology, each of thesemethods may be used in any combination therewith depending on aparticular task at hand for reconstructing a respective anatomicalstructure associated with the subject.

It should be expressly understood that not all technical effectsmentioned herein need to be enjoyed in each and every embodiment of thepresent technology.

Modifications and improvements to the above-described implementations ofthe present technology may become apparent to those skilled in the art.The foregoing description is intended to be exemplary rather thanlimiting. The scope of the present technology is therefore intended tobe limited solely by the scope of the appended claims.

1. A method for reconstructing a 3D representation of a gingiva associated with an arch form of a subject, the method being executed by a processor, the method comprising: acquiring a 3D representation of an arch form associated with the subject, the 3D representation including a representation of the gingiva of the subject; obtaining a plurality of segmentation loops, each one of the plurality of segmentation loops being representative of an interface between the gingiva and a respective tooth of the subject; determining, between each pair of adjacent segmentation loops of the plurality of segmentation loops, a midpoint, thereby generating a plurality of primary midpoints; based on the plurality of midpoints, generating a primary central curve; generating, based on the primary central curve, a first inner mesh curve and a first outer mesh curve, the first inner mesh curve positioned along a first horizontal plane and the first outer mesh curve positioned along a second horizontal plane, each one of the first horizontal plane and the second horizontal plane being spaced from at least some vertices of the plurality of segmentation loops and positioned relative thereto according to a respective predetermined position; the first inner mesh curve being offset along the first horizontal plane posteriorly relative to the plurality of segmentation loops; and the first outer mesh curve being offset along the second horizontal plane anteriorly relative to the plurality of segmentation loops; projecting the plurality of primary midpoints onto the first inner mesh curve and the first outer mesh curve, thereby generating a first plurality of inner midpoints and a first plurality of outer midpoints; generating a first segment of the reconstructed 3D representation of the gingiva by joining each one from the plurality of primary midpoints with respective ones from the first plurality of inner midpoints and from the first plurality of outer midpoints; and causing display of the first segment of the reconstructed 3D representation of the gingiva.
 2. The method of claim 1, wherein the first horizontal plane and the second horizontal plane comprise a same horizontal plane.
 3. The method of claim 1, wherein the first horizontal plane and the second horizontal plane are spaced from each other.
 4. The method of claim 1, wherein the projecting the plurality of primary midpoints onto the first inner mesh curve and the first outer mesh curve is based on respective proportional coefficients, a given one of the respective proportional coefficients being indicative of a ratio between a length of the primary central curve and that of a respective one of the first inner mesh curve and the first outer mesh curve.
 5. The method of claim 1, further comprising generating a second segment of the reconstructed 3D representation of the gingiva by: generating, based on the primary central curve, a second inner mesh curve and a second outer mesh curve, the second inner mesh curve being positioned along a third horizontal plane and the second outer mesh curve being positioned along a fourth horizontal plane, the third horizontal plane being spaced from the first horizontal plane and the fourth horizontal plane being spaced from the second horizontal plane; the second inner mesh curve being offset along the third horizontal plane posteriorly relative to the plurality of segmentation; and the second outer mesh curve being offset along the fourth horizontal plane anteriorly relative to the plurality of segmentation loops; projecting the plurality of primary midpoints onto the second inner mesh curve and the second outer mesh curve, thereby generating a second plurality of inner midpoints and a second plurality of outer midpoints; and generating the second segment of the reconstructed 3D representation of the gingiva by joining each one from the plurality of primary midpoints with respective ones from the second plurality of inner midpoints and from the second plurality of outer midpoints.
 6. The method of claim 5, further comprising causing display of the first and second segments of the reconstructed 3D representation of the gingiva.
 7. The method of claim 1, wherein the 3D representation of the arch form further includes a representation of a plurality of teeth of the subject, and the method further comprises generating each one of the plurality of segmentation loops by: generating a preliminary segmentation loop based on segmentation of respective representations of the gingiva and the plurality of teeth on the 3D representation of the arch form; identifying in the preliminary segmentation loop a plurality of vertices; and adjusting a distance between at least some of the vertices, to generate the segmentation loop.
 8. The method of claim 7, wherein the segmenting comprises applying one or more of the following functions: thresholding, clustering, edge detection, smoothing, and closing the loop.
 9. The method of claim 1, further comprising generating, between a given pair of adjacent segmentation loops of the plurality of segmentation loops, an outer arc and an inner arc for interconnecting the given pair of adjacent segmentation loops, thereby generating a primary border curve.
 10. The method of claim 9, further comprising generating, between the given pair of adjacent segmentation loops of the plurality of segmentation loops, a tween curve originating in a respective one of the plurality of primary midpoints, the tween curve extending through the outer arc and the inner arc, thereby generating a plurality of tween curves; and wherein the joining each one from the plurality of primary midpoints with respective ones from the first plurality of inner midpoints and from the first plurality of outer midpoints is based on a respective one of the plurality of tween curves.
 11. The method of claim 7, wherein the distance between the at least some of the vertices is adjusted to be equal.
 12. The method of claim 1, wherein the primary central curve is generated using a Bezier curve.
 13. The method of claim 1, further comprising using the reconstructed 3D representation of the gingiva to plan an orthodontic treatment.
 14. The method of claim 1, wherein the 3D representation of the gingiva comprises a plurality of mesh elements which are not ordered, and wherein the generated 3D representation of the gingiva comprises a plurality of ordered mesh elements.
 15. A system for reconstructing a 3D representation of a gingiva associated with an arch form of a subject, the system comprising a processor configured to execute a method, the method comprising: acquiring a 3D representation of an arch form associated with the subject, the 3D representation including a representation of the gingiva of the subject; obtaining a plurality of segmentation loops, each one of the plurality of segmentation loops being representative of an interface between the gingiva and a respective tooth of the subject; determining, between each pair of adjacent segmentation loops of the plurality of segmentation loops, a midpoint, thereby generating a plurality of primary midpoints; based on the plurality of midpoints, generating a primary central curve; generating, based on the primary central curve, a first inner mesh curve and a first outer mesh curve, the first inner mesh curve positioned along a first horizontal plane and the first outer mesh curve positioned along a second horizontal plane, each one of the first horizontal plane and the second horizontal plane being spaced from at least some vertices of the plurality of segmentation loops and positioned relative thereto according to a respective predetermined position; the first inner mesh curve being offset along the first horizontal plane posteriorly relative to the plurality of segmentation loops; and the first outer mesh curve being offset along the second horizontal plane anteriorly relative to the plurality of segmentation loops; projecting the plurality of primary midpoints onto the first inner mesh curve and the first outer mesh curve, thereby generating a first plurality of inner midpoints and a first plurality of outer midpoints; generating a first segment of the reconstructed 3D representation of the gingiva by joining each one from the plurality of primary midpoints with respective ones from the first plurality of inner midpoints and from the first plurality of outer midpoints; and causing display of the first segment of the reconstructed 3D representation of the gingiva.
 16. The system of claim 15, wherein the processor is further configured to generate a second segment of the reconstructed 3D representation of the gingiva by: generating, based on the primary central curve, a second inner mesh curve and a second outer mesh curve, the second inner mesh curve being positioned along a third horizontal plane and the second outer mesh curve being positioned along a fourth horizontal plane, the third horizontal plane being spaced from the first horizontal plane and the fourth horizontal plane being spaced from the second horizontal plane; the second inner mesh curve being offset along the third horizontal plane posteriorly relative to the plurality of segmentation; and the second outer mesh curve being offset along the fourth horizontal plane anteriorly relative to the plurality of segmentation loops; projecting the plurality of primary midpoints onto the second inner mesh curve and the second outer mesh curve, thereby generating a second plurality of inner midpoints and a second plurality of outer midpoints; and generating the second segment of the reconstructed 3D representation of the gingiva by joining each one from the plurality of primary midpoints with respective ones from the second plurality of inner midpoints and from the second plurality of outer midpoints.
 17. The system of claim 16, wherein the processor is further configured to cause display of the first and second segments of the reconstructed 3D representation of the gingiva.
 18. The system of claim 15, wherein the 3D representation of the arch form further comprises a representation of a plurality of teeth of the subject, and the processor is further configured to generate each one of the plurality of segmentation loops by: generating a preliminary segmentation loop based on segmentation of respective representations of the gingiva and the plurality of teeth on the 3D representation of the arch form; identifying in the preliminary segmentation loop a plurality of vertices; and adjusting a distance between at least some of the vertices, to generate the segmentation loop.
 19. The system of claim 15, wherein the processor is further configured to generate, between a given pair of adjacent segmentation loops of the plurality of segmentation loops, an outer arc and an inner arc for interconnecting the given pair of adjacent segmentation loops, thereby generating a primary border curve.
 20. The system of claim 19, wherein the processor is further configured to generate, between the given pair of adjacent segmentation loops of the plurality of segmentation loops, a tween curve originating in a respective one of the plurality of primary midpoints, the tween curve extending through the outer arc and the inner arc, thereby generating a plurality of tween curves; and wherein the joining each one from the plurality of primary midpoints with respective ones from the first plurality of inner midpoints and from the first plurality of outer midpoints is based on a respective one of the plurality of tween curves. 